There are two questions I wish to consider here. One is whether the diocesan monoepiscopacy is apostolic, or whether it is a post-apostolic innovation. The second question is whether episcopal and presbyterian orders were ever identical.
Regarding the first question, if we consider the evidence from the early fathers, I think the evidence is very strong that by the end of the first century, diocesan monoepiscopacy was the universal standard. (For now, just set aside the issue of the geographical extent or size of dioceses.)
Some causes for confusion on these two questions may be the following:
(1) Every bishop by office is also a presbyter (priest), but not every presbyter (priest) by office is a bishop, so there is intrinsically semantic overlap, [e.g. Archbishop Burke of St. Louis is truly a priest, though not merely a priest].
(2) There is a difference between being sacramentally ordained to the episcopal office, and being installed or appointed as the bishop in charge of a particular church/city/see. One can be given episcopal orders sacramentally without being given charge over a see.
(3) The term 'episkopos' initially also had a broader functional sense (so that [mere] presbyters could rightly be enjoined to shepherd or oversee the flock they ruled with the bishop). But by 70 AD, the terms 'presbyteros' and 'episkopos' began to be used more strictly and technically to refer to the distinct offices, i.e. the episcopal office, wherein one could consecrate the Eucharist and also ordain, and the office of [mere] presbyter, wherein one could consecrate the Eucharist, but not ordain. It is not that the office of [mere] presbyter did not initially exist and is not apostolic; it is probable that we see this office (though not formally distinguished from the episcopal office) already in various places in Acts (e.g. 11:30; 14:23; 21:18) and elsewhere in the NT, e.g. 1 Tim 5:17; James 5:14). (The episcopal office can be seen most clearly in the New Testament in Titus 1:5; 2 Tim 4:5; and 1 Tim 5:19-22. The consecration to the episcopal office can be seen in 2 Tim 1:6; and 1 Tim 4:14.) Rather, at this early point, the terms 'episkopos' and 'presbyteros' were each (and perhaps more commonly) used to refer to a type of function, as well as to the offices though without distinguishing them. Thus, from our point of view in history, at that early stage there is ambiguity with regard to the distinction in office both because every bishop is also a presbyter, and because in the functional sense of the term 'episkopos', even [mere] presbyters could rightly be said to be overseers. At the latter part of the apostolic period, we see the obvious rise of the diocesan monoepiscopate (as I'll show below), quite possibly because (a) the apostles were dying off, and so there needed to be structure in place that did not intrinsically depend upon the apostles for authority, and (b) because a group of elders each having equal authority would have been a recipe for continually schism. The other churches would most definitely have seen the bishopric of James the Righteous in Jerusalem as an exemplar. When James was killed about 62 AD, and replaced with Symeon, this too would have been an exemplar. Likewise, Evodius was ordained bishop by Peter either during Peter's first visit to Antioch (40-41 AD), or possibly during the years (50-54 AD) after the Jerusalem Council. So that too would have been an exemplar for the other churches. Paul's appointment of Timothy as bishop of Ephesus and Titus as bishop of Crete fits with the rise of the diocesan monoepiscopacy. There we possibly see the episcopal office beginning to be specified and distinguished from the office of elder (think of 1 Timothy chapter 3, and chapter 5), though (to the modern reader, at least) still quite vaguely. After the death of the apostles, we typically do not see churches without a bishop, nor, if the church had more than one bishop does it lack a head bishop. Also the growth of the churches in this period (which was apparently exponential) required bishops to fill the [mere] presbyter office in order to delegate parish responsibilities, perhaps making the use of the term 'presbyter' to refer to the office of [mere] presybter, more common, and thus disambiguating the terms and (from our point of view) distinguishing the two offices by the end of the first century. That is quite possibly why we very clearly see in the writings of Ignatius (the second bishop of Antioch and an auditor of the Apostles), written no later than 107 AD, the clear distinction between bishop and [mere] presbyter already universally recognized. The use of the term 'presbyteros' to refer to bishops continues for a long time in the early church (since, as I pointed out above, bishops are priests), but (so far as I can tell) after the New Testament era, we no longer see the term 'episkopos' used to refer to [mere] presbyters.
(4) There are apparently some cases in which the Apostles ordained more than one bishop (by office) in a single city, such that there was simultaneously two or more bishops (by office) in a single city. While there could be simultaneously more than one bishop in a local church, only one at a time was the diocesan bishop (even if the extent of the diocese was at that time merely considered to be the city in which the church was located), just as there are now two bishops at the Cathedral Basilica in Saint Louis, but only one (Archbishop Burke) is the diocesan bishop.
Those four factors, in my opinion, lead some to mistakenly conclude from the New Testament data that the office of presbyter was (and is) identical to the office of bishop. But I think a careful study of the early church and fathers does not support that conclusion. If we consider the changing needs of the Church as the apostolic era closed, then we can rightly perceive (even foreshadowed in the New Testament itself) the development of the distinction in offices. Also in cases where there was more than one bishop in a city, only one was the diocesan bishop, even where that is not stated, for the presence of a plurality of elders should not be pitted against the gospel principle "one flock, one shepherd" on the basis of an argument from silence. The major part of the evidence for there always being one head bishop is that throughout the second century, everywhere we look there is one diocesan bishop. Presumbly because of the occasion for division and schism, at least by the latter part of the first century, the rule was "one city, one [diocesan] bishop".
The second question has to be considered in light of the answer to the first question. In other words, I think that in order to find the right answer to the second question, we have to study the ecclesiastical history of the first century. The reason I say that is that in the New Testament, we do not see the two offices clearly distinguished, specifically regarding differences in powers of ordination and consecration. The most one can say (logically) from an analysis of the relevant NT passages is that there is semantic overlap. By the end of the first century, however, the offices are clearly distinguished (as we can see, for example, in the writings of Ignatius). One way to take this development is to suppose that a dreadful error occurred, such that at some point, one bishop-presbyter told some other bishop-presbyters that they were not bishop-presbyters, but rather mere presbyters, having the power to consecrate the elements but lacking the power to ordain. These bishop-presbyters accepted this 'false teaching', and the error spread all over the world by the end of the first century. A second way to explain this development is to hypothesize that some bishop-presbyter made up a new [but non-apostolic] office that supposedly but not actually gave the recipient [the power to consecrate the Eucharist but not the power to ordain]. People accepted this error, and it spread all over the world by the end of the first century, even while the Apostle John was still alive. A third way to take this development is to see it as the careful following of apostolic instructions which are not explicitly included in the New Testament. I think this third way of explaining the data is the best explanation of the data. So if one is governed by 'sola scriptura', then one may well see this development as an erroneous departure from a New Testament teaching and practice. But I think this is precisely the sort of interpretive situation that shows the problems with 'sola scriptura'. It sets up the deconstruction of the Church's development from the end of the first century to the sixteenth century, and prepares the way for the ecclesial deism that we see in, for example, Mormonism and other sects that simply write off those first 1500 or 1800 years of Church history as a giant black hole, the extended dark ages of the "Great Apostasy".
So, let's go back to the first question. And let us consider the evidence just through the first two centuries.
James the Righteous was made the diocesan bishop of Jerusalem probably in the early 40s. Notice how in Acts 21:18 reference is made to James, and then all the "elders". This James was martyred around 62 AD, being thrown off a wall and then clubbed to death. Symeon (son of the Clopas mentioned in John 19:25) succeeded him as bishop of Jerusalem. Hegesippus (110-180 AD) tells us that Symeon lived to the age of 120. Symeon remained the diocesan bishop of Jerusalem until his martyrdom in 106 or 107 AD under the emperor Trajan, after which, Eusebius tells us, a Jewish Christian named Justus was [Symeon's] successor on the cathedra of the Jerusalem bishopric. After Justus was Zacchaeus, then Tobias, then Benjamin, then John, then Matthias, then Philip, then Seneca, then Justus, then Levi, then Ephres, then Joseph, and then Judas, around the year 135 AD, when Hadrian banned all Jews from the city of Jerusalem. (Each of these bishops of the church in Jerusalem was Jewish.) Marcus was the first Gentile bishop of Jerusalem; he became bishop in 135 AD. After Marcus, the succession in the [Jerusalem] episcopate went as follows: Cassianus; after him Publius; then Maximus; following them Julian; then Gaius; after him Symmachus and another Gaius, and again another Julian; after these Capito, then Maximums II, then Antoninus, then Valens, then Dolichianus; and after all of them Narcissus." Narcissus became bishop of Jerusalem (by this time known as "Aelia Capitolina", the name given to it by Hadrian in its reconstruction) about the year 185 AD. Narcissus died around 231 AD, no less than 116 years old.
Peter ordained Evodius the first diocesan bishop of Antioch probably in the early 40s. Later Peter ordained Ignatius with episcopal orders (though Ignatius did not become the diocesan bishop of Syria until after Evodius (and presumably Peter) had died. [Ignatius describes himself as "bishop of Syria" and "bishop of Antioch".] When Ignatius died (107 AD), he was succeeded in the episcopal chair at Antioch by Heros who served in that office from 107-127, and was himself succeeded by Cornelius (127-154 AD), who was himself succeeded by Eros (154 – 169 AD), who was himself succeeded by Theophilus (169-182 AD), who wrote a book against Marcion the heretic. Theophilus was succeeded by Maximus I (182-191 AD), himself succeeded by Serapion (191-211 AD).
Mark the Evangelist was ordained the bishop of Alexandria by Peter. In Alexandria (around 62 AD) Mark ordained Annianus as its first diocesan bishop; Annianus served in that office for 22 years. After Annianus, Avilius was the diocesan bishop of Alexandria from approximately 83-97 AD, and then after him came Cerdo, who was diocesan bishop of Alexandria from 97 to 109 AD. After him Primus became diocesan bishop of Alexandria; he held that office for twelve years (109-121 AD), and was succeeded by Justus (121-129 AD), who was succeeded by Eumenes (129-141 AD), who was succeeded by Mark II (141-152 AD), who was succeeded by Celadion, (152 - 167 AD) then Agrippinus (167 – 178 AD), and then Julian (178-189 AD), and then Demetrius (189-232 AD), who died at the age of 106, and therefore was apparently born in 126 AD. Demetrius is the bishop who appointed Origen to teach at the Catechetical school in Alexandria, and then later (around 230) condemned Origen (for self-castration and, possibly, heresy). Demetrius was the first bishop of Alexandria to establish other bishoprics in Egypt.
Dionysius the Aeroapagite became the first bishop of the church in Athens. (This we learn from a letter written by a different Dionysius, Dionysius the bishop of Corinth, written around 170 AD to Soter, bishop of the church at Rome from 166-175 AD.) Dionysius the Aeroapagite was succeeded by Narkissos (who was originally from Palestine) around the year 96 AD. Narkissos was succeeded by Publius (who was from Malta). According to Jerome, Publius was martyred during the persecution under the Emperor Hadrian (117-138 AD). He was succeeded by Quadratus. There is some dispute as to whether the Quadratus who was bishop of Athens after Publius was the same Quadratus of Athens who was an apologist, and who wrote a letter to Hadrian when the latter visited the city of Athens. The letter helped relax the persecution against the Christians. In the letter he reports that he himself had seen many who were healed by Jesus and even raised from the dead by Jesus.
Paul ordained Titus the first diocesan bishop of the churches on Crete. From Dionysius, bishop of Corinth (writing in 170 AD) we learn that at that time (around 170 AD) Philip was bishop of Crete, the church at Goryna being the location of the episcopal see of Crete. It was this Philip, according to Eusebius, whose writings most effectively refuted Marcion's errors. We learn from Eusebius that Pinytus then became bishop of Crete, and died around 180. Paul also ordained Timothy the first diocesan bishop of Ephesus. Around 107 AD, Ignatius, in his epistle to the Ephesians, refers to Onesimus as the bishop of Ephesus. About 190 AD, Polycrates (born around 125 AD) the bishop of Ephesus, wrote a letter to Victor, the bishop of Rome, in which letter he tells us that the Apostle John is buried in Ephesus, and the Apostle Phillip is buried in Hieropolis. He also tells us that seven of his relatives had been bishops before him.
Hermas, mentioned in Romans 16:14, is said to have become the bishop of Philippi, and was later martyred. (His feast day is May 9.) Philemon, to whom the Apostle Paul wrote his epistle, became the bishop of Colossae, where tradition says he was martyred. The earliest tradition shows that Crescens (mentioned by Paul in 2 Tim 4:10) became a bishop in Galatia. Aristarchus, mentioned in Acts, Colossians and Philemon, became the bishop of Thessalonica. According to tradition, Jason, at whose home Paul stayed in Thessalonica (Acts 17; cf. Rom 16:21), became the bishop of Tarsus, Prochorus, one of the seven deacons named in Acts 6, became the bishop of Nicomedia, and Nicolas, another of the seven deacons, is said to have become the bishop of Samaria. But according to tradition he was led astray by Simon Magus, and gave rise to the error of the Nicolatians (referred to by John in Revelations 2:6, 15).
Philip, one of the seven deacons mentioned in Acts 6, later became the bishop of Tralles, according to Jerome. When Ignatius composed his epistles (around 107 AD), Ignatius tells us that at that time Polybius was the bishop of Tralles. Tradition says that the bishop of Philadelphia, to whom Ignatius refers without naming him in his [Ignatius's] epistle to the Philadelphians, was Demetrius (mentioned in 3 John 12). Demetrius had been ordained bishop of Philadelphia by the Apostle John. Tradition tells us that Gaius (mentioned in 3 John 1) was the first bishop of Pergamum, followed by Antipas (mentioned in Revelation 2:13). According to that tradition Antipas was martyred by being burned at the stake some time before John wrote the book of Revelation. (A piece of Antipas's skull is now preserved as a relic in the Monastery of St. John the Theologian on the island of Patmos.) Ignatius also tells us that at that time (i.e. 107 AD), Damas was the diocesan bishop of Magnesia. Papias (AD 60 - 135), an auditor of the Apostle John, and a friend of Polycarp, became the diocesan bishop of Hierapolis, the place where Philip, one of the Twelve Apostles, was buried. Two later bishops of Hierapolis were Apolinarius, who flourished during the time of Marcus Aurelius (161-180 AD), and then Abircius Marcellus, who was martyred around 200 AD. One of the men associated with Apolinarius, possibly a presbyter who had served under Apolinarius, writes to Abircius the following [excerpt from a] letter:
"Having for a very long and sufficient time, O beloved Avircius Marcellus, been urged by you to write a treatise against the heresy of those who are called after Miltiades, I have hesitated till the present time, not through lack of ability to refute the falsehood or bear testimony for the truth, but from fear and apprehension that I might seem to some to be making additions to the doctrines or precepts of the Gospel of the New Testament, which it is impossible for one who has chosen to live according to the Gospel, either to increase or to diminish. But being recently in Ancyra in Galatia, I found the church there greatly agitated by this novelty, not prophecy, as they call it, but rather false prophecy, as will be shown. Therefore, to the best of our ability, with the Lord's help, we disputed in the church many days concerning these and other matters separately brought forward by them, so that the church rejoiced and was strengthened in the truth, and those of the opposite side were for the time confounded, and the adversaries were grieved. The presbyters in the place, our fellow-presbyter Zoticus of Otrous also being present, requested us to leave a record of what had been said against the opposers of the truth." (Eusebius 5.16.1-4)
Otrous was just a few miles from Hierapolis. Zoticus was presumably the bishop of Otrous, but referred to as a "follow presbyter". That is because bishops (in office) are still presbyters, though not [mere] presbyters.
The church at Laodicea was probably founded by the Colossian Epaphras (Colossians 4:12) who was helped by Nymphan (Colossians 4:6). Its first bishop was Archippus (Col 4:17), followed by Nymphan, followed by Diotrophes (3 John 9), followed by Sagaris (who was martyred in 166 AD under Marcus Aurelius).
Polycarp (69 - 155 AD), also an auditor of the Apostle John, was made the diocesan bishop of Smyrna by that Apostle, according to both Irenaeus and Tertullian. Of Polycarp, Ireneaus writes, "But Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true." We are told by Eusebius and Jerome that in his old age Polycarp traveled to Rome and tried (unsuccessfully) to reach an agreement with Anicetus (bishop of Rome from 155-166) concerning the determination of the day on which to celebrate Easter. According to less established tradition, the first bishop of Smyrna was Apelles (mentioned in Romans 16:10), followed by Strataes, a brother (or uncle) of Timothy, then Ariston, then Bucolus, the bishop under whom Polycarp was raised, first being made a deacon, then a presbyter, and finally, upon the death of Bucolus, bishop. Polycarp became bishop of Smyrna in approximately 96 AD. In Polycarp's epistle to the Philippians, written very shortly after the death of Ignatius, Polycarp writes, "Polycarp, and the presbyters with him, to the Church of God sojourning at Philippi ...." Elsewhere in that epistle he writes, " Wherefore, it is needful to abstain from all these things, being subject to the presbyters and deacons, as unto God and Christ." After Polycarp was martyred, the next bishop of Smyrna was Papirius. Papirius was later succeeded by Camerius, who had been made a deacon by Polycarp.
Peter in Rome ordained Linus (mentioned in 2 Tim 4:;21), Anacletus and Clement (mentioned by Paul in Phil 4:3) to episcopal orders, but around the time of the death of Peter and Paul (67 AD), Linus was made the diocesan bishop of Rome and served in that episcopal seat from AD 67 - 76. Of Linus, Irenaeus (c. 130 - 200 AD) wrote: "After the Holy Apostles (Peter and Paul) had founded and set the Church in order (in Rome) they gave over the exercise of the episcopal office to Linus. The same Linus is mentioned by St. Paul in his Epistle to Timothy. His successor was Anacletus." Anacletus served as diocesan bishop of Rome from approximately 76-88, and then Clement from 88-97.
Clement, in his letter to the Corinthians, tells us that in every major city to which they traveled the Apostles appointed bishops to succeed them, and deacons [to serve these bishops]. Clement also rebukes certain of the Corinthians who had taken it upon themselves to depose several episkospoi from their office. Clement also writes, "Our apostles also knew, through our Lord Jesus Christ that there would be strife [rivalries] on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect foreknowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry. We are of opinion, therefore, that those appointed by them, or afterwards by other eminent men, with the consent of the whole church, and who have blamelessly served the flock of Christ, in a humble, peaceable, and disinterested spirit, and have for a long time possessed the good opinion of all, cannot be justly dismissed from the ministry. For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties. Blessed are those presbyters who, having finished their course before now, have obtained a fruitful and perfect departure [from this world];"
Here is Clement, the third diocesan bishop of Rome, having himself been ordained with episcopal orders by Peter, explaining that the Apostles knew there would be strife on account of the episcopal office, and that therefore they gave instructions regarding succession and replacement of bishops. There would indeed have been strife on account of the episcopal office, and rampant schism, if each of the bishops in a city were simultaneously diocesan bishop. By having a single diocesan bishop, the church at Rome would have been continually violating the Apostles' instructions for over twenty years, since the deaths of Peter and Paul. Notice also that the episcopal office was typically for life. Notice also that the ordinary replacement for a diocesan bishop was someone appointed by that bishop, or, if the diocesan bishop had already died, then the appointment was made by "other eminent men" (i.e. other bishops) with the consent of the whole church.
It is helpful also here at this point to consider the Didache, which is a very early document, probably written around 50-70 AD, maybe even earlier. The relevant passage here is, "Appoint, therefore, for yourselves, bishops and deacons worthy of the Lord, men meek, and not lovers of money, and truthful and proved; for they also render to you the service of prophets and teachers. Despise them not therefore, for they are your honoured ones, together with the prophets and teachers." This passage should not be taken to mean that laymen could ordain. Rather, it should be understood in the context of the other descriptions of ordination we see in the early church, such as the one given by Clement. In these other cases, the people put forward those whom they wished to be ordained. But the ordination itself was not done by laymen. Similarly, the two-fold distinction between bishops and deacons, made both here in the Didache and in Clement, should not be taken as denying [mere] presbyterian orders. The two-fold distinction in orders [bishops and deacons] is centered around the Eucharist, between orders that can and orders that cannot offer the Eucharist. As Ignatius says of the deacons in his epistle to the Trallians, "For they [deacons] are not ministers of meat and drink". The model for the selection of deacons is found in Acts 6, wherein we find that the Apostles told the disciples to select from among themselves candidates for the office of deacon, and then these men were brought before the Apostles, and ordained to the deaconate office by the Apostles. This same model seems to have been followed everywhere, and not just with deacons, but also with presbyters and bishops. The candidate is selected by the people, and then ordained by the bishop(s).
Clement does allude to the three-fold distinction in orders. In chapter 40 of his letter to the Corinthians, he writes, "These things therefore being manifest to us, and since we look into the depths of the divine knowledge, it behooves us to do all things in [their proper] order, which the Lord has commanded us to perform at stated times. He has enjoined offerings [to be presented] and service to be performed [to Him], and that not thoughtlessly or irregularly, but at the appointed times and hours. Where and by whom He desires these things to be done, He Himself has fixed by His own supreme will, in order that all things, being piously done according to His good pleasure, may be acceptable unto Him. Those, therefore, who present their offerings at the appointed times, are accepted and blessed; for inasmuch as they follow the laws of the Lord, they sin not. For his own peculiar services are assigned to the high priest, and their own proper place is prescribed to the priest, and their own special ministrations devolve on the Levites. The layman is bound by the laws that pertain to layman." Clement's three-fold distinction of orders is not accidental. It is intended to provide a parallel for the three Christian orders. For even in the Didache we see this: "Every first-fruit, therefore, of the products of wine-press and threshing-floor, of oxen and of sheep, you shall take and give to the prophets, for they are your high priests." But when the age of apostles and prophets was over, then this role of high priest fell to the bishops. Similarly, the Didache refers to the Eucharist in sacrificial language: "But let no one that is at variance with his fellow come together with you, until they be reconciled, that your sacrifice may not be profaned. For this is that which was spoken by the Lord: In every place and time offer to me a pure sacrifice; for I am a great King, says the Lord, and my name is wonderful among the nations." This notion of Eucharistic sacrifice helps us connect Clement's reference to the three-fold priestly orders of the Old Covenant, to his understanding of its continuation under the New Covenant.
At Clement's death in 97 AD, he was succeeded by Evaristus, who served as diocesan bishop of Rome from 97 to 105 AD. After the death of Evaristus, Alexander became diocesan bishop of Rome, and served in that office for ten years, until 115 AD. He was succeeded by Xystus, who held that office until 125 AD, and then Telesphorus, from 125 AD to 136 AD at which time he died as a martyr, and then Hyginus held the office from 136 to 140 AD. Then Pius from 140 to 155 AD. Then Anicetus (155-166), whom as I mentioned above was sought out by Polycarp regarding the date of Easter. After Anicetus, Soter sat in the episcopal seat in Rome from 166-175 AD. Then Eleutherius from 175-189 AD. Then Victor from 189-199 AD. And then Zephyrinus from 199-217 AD.
Next consider the narrative of the Apostle John in Ephesus, in the work by Clement of Alexandria (d. 215) titled, "The Rich Man Who Finds Salvation". Clement writes, "And that you may be still more confident, that repenting thus truly there remains for you a sure hope of salvation, listen to a tale, which is not a tale but a narrative, handed down and committed to the custody of memory, about the Apostle John. For when, on the tyrant's death, he returned to Ephesus from the isle of Patmos, he went away, being invited, to the contiguous territories of the nations, here to appoint bishops, there to set in order whole Churches, there to ordain such as were marked out by the Spirit. Having come to one of the cities not far off (the name of which some give), and having put the brethren to rest in other matters, at last, looking to the bishop appointed, and seeing a youth, powerful in body, comely in appearance, and ardent, said, "This (youth) I commit to you in all earnestness, in the presence of the Church, and with Christ as witness." And on his accepting and promising all, he gave the same injunction and testimony. And he set out for Ephesus. And the presbyter taking home the youth committed to him, reared, kept, cherished, and finally baptized him. After this he relaxed his stricter care and guardianship, under the idea that the seal of the Lord he had set on him was a complete protection to him. .... Time passed, and some necessity having emerged, they send again for John. He, when he had settled the other matters on account of which he came, said, "Come now, O bishop, restore to us the deposit which I and the Saviour committed to you in the face of the Church over which you preside, as witness."
Ignatius, bishop of Antioch, (martyred in Rome around 107 AD) clearly distinguishes between bishops and presbyters, treating bishops with greater authority than [mere] presbyters (i.e. presbyters who are not bishops).
Ignatius, in his epistle to the Ephesians, refers to Onesimus as the bishop of the Ephesians (chptr 1). Then Ignatius says, "It is therefore befitting that you should in every way glorify Jesus Christ who has glorified you, that by a unanimous obedience you may be perfectly joined together in the same mind, and in the same judgment, and may all speak the same thing concerning the same thing,"1 Corinthians 1:10 and that, being subject to the bishop and the presbytery, you may in all respects be sanctified." (chptr 2) Ignatius speaks of bishops being already established all over the world. He says, "For even Jesus Christ, our inseparable life, is the [manifested] will of the Father; as also bishops, settled everywhere to the utmost bounds [of the earth], are so by the will of Jesus Christ." (chptr 3) Then he goes on in chapter 4, "Wherefore it is fitting that you should run together in accordance with the will of your bishop, which thing also you do. For your justly renowned presbytery, worthy of God, is fitted as exactly to the bishop as the strings are to the harp." Then in chapter 5, "For if I in this brief space of time, have enjoyed such fellowship with your bishop —I mean not of a mere human, but of a spiritual nature—how much more do I reckon you happy who are so joined to him as the Church is to Jesus Christ, and as Jesus Christ is to the Father, that so all things may agree in unity!" And then in that same chapter, " Let us be careful, then, not to set ourselves in opposition to the bishop, in order that we may be subject to God." Then in chapter six he writes, " Now the more any one sees the bishop keeping silence, the more ought he to revere him. For we ought to receive every one whom the Master of the house sends to be over His household, Matt 24:25 as we would do Him that sent him. It is manifest, therefore, that we should look upon the bishop even as we would upon the Lord Himself. And indeed Onesimus himself greatly commends your good order in God, that you all live according to the truth, and that no sect has any dwelling-place among you. Nor, indeed, do ye hearken to any one rather than to Jesus Christ speaking in truth." Then in chapter 20 he writes, "so that ye obey the bishop and the presbytery with an undivided mind, breaking one and the same bread, which is the medicine of immortality, and the antidote to prevent us from dying, but [which causes] that we should live for ever in Jesus Christ."
In his letter to the Magnesians, chapter 2, Ignatius writes, "Since, then, I have had the privilege of seeing you, through Damas your most worthy bishop, and through your worthy presbyters Bassus and Apollonius, and through my fellow-servant the deacon Sotio, whose friendship may I ever enjoy, inasmuch as he is subject to the bishop as to the grace of God, and to the presbytery as to the law of Jesus Christ, [I now write to you]." In chapter 3, he writes, "Now it becomes you also not to treat your bishop too familiarly on account of his youth, but to yield him all reverence, having respect to the power of God the Father, as I have known even holy presbyters do, not judging rashly, from the manifest youthful appearance [of their bishop], but as being themselves prudent in God, submitting to him, or rather not to him, but to the Father of Jesus Christ, the bishop of us all. It is therefore fitting that you should, after no hypocritical fashion, obey [your bishop] in honour of Him who has willed us [so to do], since he that does not so deceives not [by such conduct] the bishop that is visible, but seeks to mock Him that is invisible. And all such conduct has reference not to man, but to God, who knows all secrets." In chapter 4 he writes, " It is fitting, then, not only to be called Christians, but to be so in reality: as some indeed give one the title of bishop, but do all things without him. Now such persons seem to me to be not possessed of a good conscience, seeing they are not stedfastly gathered together according to the commandment." In chapter 6 he writes, "Since therefore I have, in the persons before mentioned, beheld the whole multitude of you in faith and love, I exhort you to study to do all things with a divine harmony, while your bishop presides in the place of God, and your presbyters in the place of the assembly of the apostles, along with your deacons, who are most dear to me, and are entrusted with the ministry of Jesus Christ, who was with the Father before the beginning of time, and in the end was revealed. Do ye all then, imitating the same divine conduct, pay respect to one another, and let no one look upon his neighbour after the flesh, but do ye continually love each other in Jesus Christ. Let nothing exist among you that may divide you; but be ye united with your bishop, and those that preside over you, as a type and evidence of your immortality." In chapter 7 he writes, "As therefore the Lord did nothing without the Father, being united to Him, neither by Himself nor by the apostles, so neither do ye anything without the bishop and presbyters. Neither endeavour that anything appear reasonable and proper to yourselves apart; but being come together into the same place, let there be one prayer, one supplication, one mind, one hope, in love and in joy undefiled." In chapter 13 he writes, "with your most admirable bishop, and the well-compacted spiritual crown of your presbytery, and the deacons who are according to God. Be subject to the bishop, and to one another, as Jesus Christ to the Father, according to the flesh, and the apostles to Christ, and to the Father, and to the Spirit; that so there may be a union both fleshly and spiritual." In chapter 15 he writes, "The Ephesians from Smyrna (whence I also write to you), who are here for the glory of God, as you also are, who have in all things refreshed me, salute you, along with Polycarp, the bishop of the Smyrnæans."
In his epistle to the Trallians, Ignatius writes in chapter 1, "I know that you possess an unblameable and sincere mind in patience, and that not only in present practice, but according to inherent nature, as Polybius your bishop has shown me, who has come to Smyrna by the will of God and Jesus Christ, and so sympathized in the joy which I, who am bound in Christ Jesus, possess, that I beheld your whole multitude in him." In chapter 2, he writes, "For, since you are subject to the bishop as to Jesus Christ, you appear to me to live not after the manner of men, but according to Jesus Christ, who died for us, in order, by believing in His death, you may escape from death. It is therefore necessary that, as you indeed do, so without the bishop you should do nothing, but should also be subject to the presbytery, as to the apostle of Jesus Christ, who is our hope, in whom, if we live, we shall [at last] be found. It is fitting also that the deacons, as being [the ministers] of the mysteries of Jesus Christ, should in every respect be pleasing to all. For they are not ministers of meat and drink, but servants of the Church of God. They are bound, therefore, to avoid all grounds of accusation [against them], as they would do fire." In chapter 3 he writes, "In like manner, let all reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the sanhedrim of God, and assembly of the apostles. Apart from these, there is no Church. Concerning all this, I am persuaded that you are of the same opinion. For I have received the manifestation of your love, and still have it with me, in your bishop, whose very appearance is highly instructive, and his meekness of itself a power; whom I imagine even the ungodly must reverence, seeing they are also pleased that I do not spare myself. But shall I, when permitted to write on this point, reach such a height of self-esteem, that though being a condemned man, I should issue commands to you as if I were an apostle?" In chapter 7 he writes, "Be on your guard, therefore, against such persons. And this will be the case with you if you are not puffed up, and continue in intimate union with Jesus Christ our God, and the bishop, and the enactments of the apostles. He that is within the altar is pure, but he that is without is not pure; that is, he who does anything apart from the bishop, and presbytery, and deacons, such a man is not pure in his conscience." In chapter 12, he writes, "Continue in harmony among yourselves, and in prayer with one another; for it becomes every one of you, and especially the presbyters, to refresh the bishop, to the honour of the Father, of Jesus Christ, and of the apostles." In chapter 13 he writes, "Fare well in Jesus Christ, while you continue subject to the bishop, as to the command [of God], and in like manner to the presbytery."
In his epistle to the Romans, Ignatius writes in chapter 2, "that God has deemed me, the bishop of Syria, worthy to be sent for from the east unto the west."
In his epistle to the Philadelphians, Ignatius writes in chapter 2, "Wherefore, as children of light and truth, flee from division and wicked doctrines; but where the shepherd is, there follow as sheep. For there are many wolves that appear worthy of credit, who, by means of a pernicious pleasure, carry captive (2 Timothy 3:6) those that are running towards God; but in your unity they shall have no place." In chapter 3 he writes, "Keep yourselves from those evil plants which Jesus Christ does not tend, because they are not the planting of the Father. Not that I have found any division among you, but exceeding purity. For as many as are of God and of Jesus Christ are also with the bishop. And as many as shall, in the exercise of repentance, return into the unity of the Church, these, too, shall belong to God, that they may live according to Jesus Christ. Do not err, my brethren. If any man follows him that makes a schism in the Church, he shall not inherit the kingdom of God. If any one walks according to a strange opinion, he agrees not with the passion [of Christ.]." In chapter 4, he writes, "Take heed, then, to have but one Eucharist. For there is one flesh of our Lord Jesus Christ, and one cup to [show forth] the unity of His blood; one altar; as there is one bishop, along with the presbytery and deacons, my fellow-servants: that so, whatsoever you do, you may do it according to [the will of] God.." In chapter 7, he writes, "For, when I was among you, I cried, I spoke with a loud voice: Give heed to the bishop, and to the presbytery and deacons. Now, some suspected me of having spoken thus, as knowing beforehand the division caused by some among you. But He is my witness, for whose sake I am in bonds, that I got no intelligence from any man. But the Spirit proclaimed these words: Do nothing without the bishop; keep your bodies as the temples of God; love unity; avoid divisions; be the followers of Jesus Christ, even as He is of His Father." In chapter 8 he writes, "I therefore did what belonged to me, as a man devoted to unity. For where there is division and wrath, God does not dwell. To all them that repent, the Lord grants forgiveness, if they turn in penitence to the unity of God, and to communion with the bishop." In chapter 10 he writes, "as also the nearest Churches have sent, in some cases bishops, and in others presbyters and deacons."
In epistle to the Smyrnaeans, Ignatius writes in chapter 8, "See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid." In chapter 9, he writes, "It is well to reverence both God and the bishop. He who honours the bishop has been honoured by God; he who does anything without the knowledge of the bishop, does [in reality] serve the devil." In chapter 12 he writes, "I salute your most worthy bishop, and your very venerable presbytery, and your deacons, my fellow-servants, and all of you individually, as well as generally, in the name of Jesus Christ, and in His flesh and blood, in His passion and resurrection, both corporeal and spiritual, in union with God and you."
In his epistle to Polycarp, Ignatius writes in chapter 5, "If he begins to boast, he is undone; and if he reckon himself greater than the bishop, he is ruined." In chapter 6 he writes, "Give heed to the bishop, that God also may give heed to you. My soul be for theirs that are submissive to the bishop, to the presbyters, and to the deacons, and may my portion be along with them in God!" In chapter 7 he writes, "It is fitting, O Polycarp, most blessed in God, to assemble a very solemn council, and to elect one whom you greatly love, and know to be a man of activity, who may be designated the messenger of God; and to bestow on him this honour that he may go into Syria, and glorify your ever active love to the praise of Christ."
Shepherd of Hermas (probably middle second century, maybe earlier); Vision 3, Chapter 5, "Hear now with regard to the stones which are in the building. Those square white stones which fitted exactly into each other, are apostles, bishops, teachers, and deacons, who have lived in godly purity, and have acted as bishops and teachers and deacons chastely and reverently to the elect of God. Some of them have fallen asleep, and some still remain alive. And they have always agreed with each other, and been at peace among themselves, and listened to each other. On account of this, they join exactly into the building of the tower."
It may be helpful to think of Marcion's church. Marcion's father was a bishop of Sinope in Pontus. Marcion was born around 110 AD, and was made a bishop (but not the diocesan bishop) in his home town. He was eventually expelled from his own church by his father, when he committed a grave sin with a virgin. He traveled to Rome, arriving sometime around 140 AD. In 144 AD he was excommunicated from the church at Rome by Pius, the bishop of Rome (said to be the brother of Hermas who wrote "Shepherd of Hermas"). Marcion started his own church, with bishops, priests, and deacons. Marcion didn't just make up this three-fold hierarchical order in his church; he got it from the Catholic church from which he was expelled. Moreover, had he not been a bishop, he could not have instituted three-fold orders, for he would not have had the charism needed to ordain anyone in his church.
The first bishop of Lyon was Pothinus (b. 87; d. 177 AD). He was martyred under the persecution of Marcus Aurelius. He was succeeded by Irenaeus (130? – 202 AD), who had been a priest (presbyter) in Lyon under bishop Pothinus, and had been sent to Eleutherus (bishop of Rome from 175-189 AD), to help bring some relief from the persecution. Irenaeus was himself from Smyrna, and had been a pupil under Polycarp, making Irenaeus only one generation removed from the Apostles. Irenaeus served as bishop of Lyon from approximately 177 – 202 AD). Irenaeus writes, "Anyone who wishes to discern the truth may see in every church in the whole world the Apostolic tradition clear and manifest. We can enumerate those who were appointed as bishops in the churches by the Apostles and their successors to our own day, who never knew and never taught anything resembling their (that is, the Gnostics') foolish doctrine. Had the Apostles known any such mysteries, which they taught privately and sub rosa to the perfect, they would surely have entrusted this teaching to the men in whose charge they placed the Churches. For they wished them to be without blame and reproach to whom they handed over their own position of authority." He continues, " Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; [we do this, I say,] by indicating that tradition derived from the apostles ...." Notice that Irenaeus is saying that lists of episcopal succession are available, so available in fact, that including them all would go beyond his purpose in his book. See here.
Irenaeus tells us that Christians refute the heretics specifically by appealing to the Apostolic succession of bishops. The heretics are not successors of the Apostles and they do not have the charism of truth. A little further he writes, "It is necessary to obey those who are the presbyters in the Church, those who, as we have shown, have succession from the apostles; those who have received, with the succession of the episcopate, the sure charism of truth according to the good pleasure of the Father. But the rest, who have no part in the primitive succession and assemble wheresoever they will, must be held in suspicion". See here. Irenaeus shows that presbyters must have apostolic succession, and they must have it through the succession the episcopate, that is, from bishops who are successors of the Apostles.
Irenaeus also writes: "Now all these [heretics] are of much later date than the bishops to whom the apostles committed the Churches; which fact I have in the third book taken all pains to demonstrate. It follows, then, as a matter of course, that these heretics aforementioned, since they are blind to the truth, and deviate from the [right] way, will walk in various roads; and therefore the footsteps of their doctrine are scattered here and there without agreement or connection. But the path of those belonging to the Church circumscribes the whole world, as possessing the sure tradition from the apostles, and gives unto us to see that the faith of all is one and the same, since all receive one and the same God the Father, and believe in the same dispensation regarding the incarnation of the Son of God, and are cognizant of the same gift of the Spirit, and are conversant with the same commandments, and preserve the same form of ecclesiastical constitution, and expect the same advent of the Lord, and await the same salvation of the complete man, that is, of the soul and body." See here.
Hegesippus (110-180 AD), who visited Rome during the time between the bishoprics of Anicetus and Eleutherius, i.e. 155-189 AD, writes, "In every line of bishops and in every city things accord with the preaching of the Law, Prophets, and the Lord." He regards the unbroken succession of bishops as the guarantee of truth.
About 190 AD, Polycrates, the bishop of Ephesus, tells us of Thraseas, the bishop and martyr from Eumenia. He tells us of Melito (117? – 180 AD), the bishop of Sardis. It was this bishop Melito who first produced a list of the accepted books of the Old Testament. Polycrates also tells us of Paparius, the bishop who succeeded Polycarp in Smyrna. Primus was the bishop of Corinth around 155 AD. He was succeeded as bishop by Dionysius, who tells us in a letter written about 170 AD that Palmas was the bishop of Amastris and Pontus, that Pinytus was the bishop of the Gnossians (also spelled 'Cnossians') in Crete. Eusebius tells us that at this time (during the reign of Marcus Aurelius, i.e. 161-180 AD), Apolinarius was the bishop of Hierapolis, and wrote against the Montanists. Apolinarius tells us of Julian, the bishop of Apamea, Sotas the bishop of Anchialus, and Julias the bishop of Thrace. After Dionysius (bishop of Corinth c. 170 AD), we see Theophilus as the bishop of Corinth in the last decade of the second century (189-199 AD), along with Cassius, the bishop of Tyre, and Clarus, the bishop of Ptolemais.
Clement of Alexandria writes (before 202 AD), "A multitude of other pieces of advice to particular persons is written in the holy books: some for presbyters, some for bishops and deacons; and others for widows, of whom we shall have opportunity to speak elsewhere" (The Instructor of Children 3:12:97:2).
Sometime after 202 AD Clement of Alexandria writes, "Even here in the Church the gradations of bishops, presbyters, and deacons happen to be imitations, in my opinion, of the angelic glory and of that arrangement which, the Scriptures say, awaits those who have followed in the footsteps of the apostles and who have lived in complete righteousness according to the gospel" (Stromateis 6:13:107:2)
Apostolic Tradition (215 AD) This was written by Hippolytus of Rome (170-236 AD), and in it he provides the consecration rites for all three orders. His purpose in writing them is to preserve a long-standing tradition. You can read each of the three ordination rites here. (Then, if you wish, compare them to the Catholic Church's present-day ordination rites here.) Hippolytus writes: "Let the bishop be ordained after he has been chosen by all the people. When someone pleasing to all has been named, let the people assemble on the Lord's Day with the presbyters and with such bishops as may be present. All giving assent, the bishops shall impose hands on him and the presbyters shall stand by in silence. Indeed, all shall remain silent, praying in their hearts for the descent of the Spirit" (The Apostolic Tradition 2:1 [A.D. 215]) Notice that the presbyters stand by in silence at the ordination of a bishop. But, Hippolytus shows that at the ordination of a [mere] presbyter (i.e. a presbyter who is not also a bishop), a bishop is necessary, but the presbyters present also lay their hands on the one being ordained. At the ordination of a deacon, however, only a bishop lays on his hand. (This is still how it is done in the Catholic Church today.)
Hippolytus provides this explanation: "When one ordains a deacon, he is chosen according to what has been said above, with only the bishop laying on his hand in the same manner. In the ordination of a deacon, only the bishop lays on his hand, because the deacon is not ordained to the priesthood, but to the service of the bishop, to do that which he commands. For he is not part of the council of the clergy, but acts as a manager, and reports to the bishop what is necessary. He does not receive the spirit common to the elders, which the elders share, but that which is entrusted to him under the bishop's authority. This is why only the bishop makes a deacon. Upon the elders, the other elders place their hands because of a common spirit and similar duty. Indeed, the elder has only the authority to receive this, but he has no authority to give it. Therefore he does not ordain to the clergy. Upon the ordination of the elder he seals; the bishop ordains."
Origen (around 235 AD) writes, "Not fornication only, but even marriages make us unfit for ecclesiastical honors; for neither a bishop, nor a presbyter, nor a deacon, nor a widow is able to be twice married" (Homilies on Luke, number 17).
See also the letter Cornelius (bishop of Rome from 251-253 AD) wrote to Bishop Fabius of Antioch, regarding the means by which Novatus got himself ordained a bishop (recorded in Eusebius 6.43). He basically got together some bishops from other cities, and got them drunk, in order to get them to ordain him. The story is appalling, of course, but again it shows his understanding that [mere] presbyters could not ordain; bishops were necessary for ordination.
Council of Elvira (300 AD)
Canon 18: "Bishops, presbyters, and deacons may not leave their own places for the sake of commerce, nor are they to be traveling about the provinces, frequenting the markets for their own profit. Certainly for the procuring of their own necessities they can send a boy or a freedman or a hireling or a friend or whomever, but, if they wish to engage in business, let them do so within the province".
Council of Nicaea (325 AD)
Protestants have typically taken the creed formulated by this council as at least instructive, if not authoritative, but then tended to ignore the canons decreed by this council. It is also important to remember that the bishops here were not being innovators. For the most part, they were attempting to formalize what had always been standard belief and practice in their respective sees.
Canon 3: "The great Synod has stringently forbidden any bishop, presbyter, deacon, or any one of the clergy whatever, to have a subintroducta dwelling with him, except only a mother, or sister, or aunt, or such persons only as are beyond all suspicion."
Canon 4: "It is by all means proper that a bishop should be appointed by all the bishops in the province; but should this be difficult, either on account of urgent necessity or because of distance, three at least should meet together, and the suffrages of the absent [bishops] also being given and communicated in writing, then the ordination should take place."
Canon 8: "But if they [Cathari] come over [to the Catholic church] where there is a bishop or presbyter of the Catholic Church, it is manifest that the Bishop of the Church must have the bishop's dignity; and he who was named bishop by those who are called Cathari shall have the rank of presbyter, unless it shall seem fit to the Bishop to admit him to partake in the honour of the title. Or, if this should not be satisfactory, then shall the bishop provide for him a place as Chorepiscopus, or presbyter, in order that he may be evidently seen to be of the clergy, and that there may not be two bishops in the city.
Canon 18: " It has come to the knowledge of the holy and great Synod that, in some districts and cities, the deacons administer the Eucharist to the presbyters, whereas neither canon nor custom permits that they who have no right to offer should give the Body of Christ to them that do offer. And this also has been made known, that certain deacons now touch the Eucharist even before the bishops. Let all such practices be utterly done away, and let the deacons remain within their own bounds, knowing that they are the ministers of the bishops and the inferiors of the presbyters. Let them receive the Eucharist according to their order, after the presbyters, and let either the bishop or the presbyter administer to them. Furthermore, let not the deacons sit among the presbyters, for that is contrary to canon and order. And if, after this decree, any one shall refuse to obey, let him be deposed from the diaconate."
Synod at Antioch (341 AD) This synod demanded the presence of at least the majority of the bishops of the province at episcopal ordinations.
Apostolic Constitutions: (compiled around the middle of the fourth century): "Let a bishop be ordained by three or two bishops; but if any one be ordained by one bishop, let him be deprived, both himself and he that ordained him. But if there be a necessity that he have only one to ordain him, because more bishops cannot come together, as in time of persecution, or for such like causes, let him bring the suffrage of permission from more bishops." (Canon 27)
Council of Trent:
Session 23, Chapter 4; July 15, 1563: "But, forasmuch as in the sacrament of Order, as also in Baptism and Confirmation, a character is imprinted, which can neither be effaced nor taken away; the holy Synod with reason condemns the opinion of those, who assert that the priests of the New Testament have only a temporary power; and that those who have once been rightly ordained, can again become laymen, if they do not exercise the ministry of the word of God. And if any one affirm, that all Christians indiscrimately are priests of the New Testament, or that they are all mutually endowed with an equal spiritual power, he clearly does nothing but confound the ecclesiastical hierarchy, which is as an army set in array; as if, contrary to the doctrine of blessed Paul, all were apostles, all prophets, all evangelists, all pastors, all doctors. Wherefore, the holy Synod declares that, besides the other ecclesiastical degrees, bishops, who have succeeded to the place of the apostles, principally belong to this hierarchial order; that they are placed, as the same apostle says, by the Holy Ghost, to rule the Church of God; that they are superior to priests; administer the sacrament of Confirmation; ordain the ministers of the Church; and that they can perform very many other things; over which functions others of an inferior order have no power. Furthermore, the sacred and holy Synod teaches, that, in the ordination of bishops, priests, and of the other orders, neither the consent, nor vocation, nor authority, whether of the people, or of any civil power or magistrate whatsoever, is required in such wise as that, without this, the ordination is invalid: yea rather doth It decree, that all those who, being only called and instituted by the people, or by the civil power and magistrate, ascend to the exercise of these ministrations, and those who of their own rashness assume them to themselves, are not ministers of the church, but are to be looked upon as thieves and robbers, who have not entered by the door. These are the things which it hath seemed good to the sacred Synod to teach the faithful in Christ, in general terms, touching the sacrament of Order. But It hath resolved to condemn whatsoever things are contrary thereunto, in express and specific canons, in the manner following; in order that all men, with the help of Christ, using the rule of faith, may, in the midst of the darkness of so many errors, more easily be able to recognise and to hold Catholic truth.
Canon 6: "If any one saith, that, in the Catholic Church there is not a hierarchy by divine ordination instituted, consisting of bishops, priests, and ministers; let him be anathema."
Canon 7: "If any one saith, that bishops are not superior to priests; or, that they have not the power of confirming and ordaining; or, that the power which they possess is common to them and to priests; or, that orders, conferred by them, without the consent, or vocation of the people, or of the secular power, are invalid; or, that those who have neither been rightly ordained, nor sent, by ecclesiastical and canonical power, but come from elsewhere, are lawful ministers of the word and of the sacraments; let him be anathema."
Wherever we look in the church of the latter first century through second century, we see diocesan monoepiscopacy. We don't see cases where there are (explicitly) [mere] presbyters but no bishops, or bishops but no head [diocesan] bishop. Nor do we see presbyters who are not also bishops, ordaining anyone. In the early church, the ordination of a bishop typically involved bishops from the surrounding cities. Moreover, what is striking in a big-picture overview of the first two centuries is the continuity from the first century onward. The three orders are already present at the end of the first century. And nothing in the writing of the fathers suggests that Ignatius's understanding of the three orders was not the universal norm.
I recommend the article titled Bishop in the Catholic Encyclopedia. I also recommend the entry "Hierarchy of the Early Church" in the Catholic Encyclopedia. One place in that article reads, "The Divine institution of the threefold hierarchy cannot of course be derived from our [Scripture] texts; in fact it cannot in any way be proved directly from the New Testament; it is Catholic dogma by virtue of dogmatic tradition, i.e. in a later period of ecclesiastical history the general belief in the Divine institution of the episcopate, presbyterate, and diaconate can be verified and thence be followed on through the later centuries. But this dogmatic truth cannot be traced back to Christ Himself by analysis of strictly historical testimony."
A few final and related points: First, how could we trust the determinations of the Ecumenical Councils if we presume that from the first century the bishops were mistaken on such a fundamental point, namely, that there is no [mere] presbyter order? Second, the distinction between bishops and [mere] presbyters is fundamentally a matter of Church dogma, decreed as such by the Church at the Council of Trent, in response to the rejection of the distinction by Protestants. (The Council of Trent did not answer the question: Is the superiority of bishops to presbyters an institution by Christ directly or by the Church. But any Church dogma is understood as a truth immediately (formally) revealed by God which has been proposed by the Teaching Authority of the Church to be believed as such.) Therefore, if we claim that [mere] presbyters, can ordain, we are essentially presupposing that the Church has no authority, that when the Church speaks definitively and authoritatively, Christians may rebel against her without sinning.
why did Luther think [mere] presbyters could ordain? It is important to
remember that no Catholic bishops joined Luther (at least initially). But to
keep up his movement, Luther needed additional priests. So Luther performed the
first 'Evangelical ordination' in May of 1525. Many of the things that Luther
said were things the Church needed to hear; honest Catholics are the first to
admit it. But in my opinion, what Luther did in May of 1525 was his gravest
error. How did he justify this action? By appealing to Scripture, of course,
but also to a letter written by Jerome in which Jerome intended to show that
deacons are not equal to presbyters, but did so by in certain respects,
equating presbyters and bishops. You can read that passage here. The problem with
the Jerome letter is that it is very easily misunderstood. In Catholic
theology, bishop and priests are indeed the same in a certain respect. They are
in one class, and deacons are in another. Bishops are indeed in the class of
priests, as I have said earlier. But bishops are also not mere priests, since,
as Jerome acknowledges, bishops (but not mere priests) possess the power of
ordination and jurisdiction. As for the early ordination practice of the
Alexandrian church, what Luther apparently did not understand is that those
'presbyters' in Alexandria, were not [mere] presbyters, but were
presbyter-bishops. And hence these ordinations were still valid. Here is a
relevant section from the Catholic Encyclopedia article titled,
"We may not dismiss the question without recalling the use which Presbyterians, since Selden, have made of that tradition to uphold their views on the early organization of the Church. It suffices to say that their theory rests, after all, on the gratuitous assumption (to put it as mildly as possible) that the presbyters who used to elect the Bishop of Alexandria, were priests as understood in the now current meaning of this word. Such is not the tradition; according to Eutychius himself, Selden's chief authority, the privilege of patriarchal election was vested not in the priests in general, but in a college of twelve priests on whom that power had been conferred by St. Mark. They were in that sense an episcopal college. Later on, when it became necessary to establish resident bishops in the provinces, the appointees may have been selected from the college of presbyters, while still retaining their former quality of members of the episcopal college. So that, little by little, the power of patriarchal election passed into the hands of regular bishops. The transfer would have been gradual and natural; which would explain the incertitude of the witnesses of the tradition as to the time when the old order of things disappeared. Eutychius may have been influenced in his statement by the fourth Nicene canon. As for St. Jerome, he may have meant Demetrius and Heraclas, instead of Heraclas and Dionysius, for he may have been aware of the other tradition handed down by Eutychius, to the effect that those two patriarchs were the first to ordain bishops since St. Mark." (See here.)
The problem for Luther is this: Luther's orders were the orders of a [mere] presbyter, whereas the orders of the Alexandrian presbyters were the orders of presbyter-bishops. Of course Luther could appeal to Scripture to deny the distinction between the two orders of bishop and [mere] presbyter. But that just leads us back to the original question: Whose interpretation of Scripture [and determination of theology] is authoritative? That of the Sacred Magisterium, or that of Luther? It is not even clear (to me) that Luther believed that a validly ordained priest must perform or be present at an ordination. Luther simply denied altogether that ordination was a sacrament, i.e. a means of grace. Luther viewed ordination as "a simple calling to the service of preaching and the administration of the sacraments. The laying-on of hands with prayer in a solemn congregational service was considered a fitting human rite." (See here.) Calvin likewise, was not a Catholic priest. It seems to me, from my reading of the Reformers, that their emphasis was on the priesthood of all believers, without any [sacramental] distinction between clerics and laymen. With regard to sacramental orders, I don't even see in the Reformation an attempt at a 'middle' road between "priesthood of all believers" on the one hand, and the Catholic position on the other hand. That is, I don't see Protestants arguing that because gifts are transferred at ordination, therefore the presence of one already ordained is necessary at any ordination. The notion of the priesthood of all believers (all sharing in that priesthood in equal measure), in principle reduced ordination to only a formal recognition of a particular vocation, not a sacramental act.
It appears to me that Protestant ordinations (Anglicanism excepted) were from the very beginning based on the principle of the "priesthood of all believers", such that there is no need whatsoever for any line of succession, since every believer [as such] already has all that is necessary [spiritually, if not intellectually and/or vocationally] to be a presbyter. In other words, excepting Anglicanism, it seems to me that the Protestant understanding of the priesthood of all believers rules out the possibility of SGA, and thus entails DGA. To be clear, the Catholic Church also recognizes the priesthood of all believers, as you can see here and here. That is called the "baptismal priesthood". But in Catholic theology, contrary to Protestant theology (again, Anglicanism excepted), the "ministerial priesthood" is not the same as the "baptismal priesthood", as you can see here.
 As for why Polycarp does not formally address a bishop in his letter to the Philippians, I simply don't know the answer to that question. There are a number of possible explanations, but I don't think it would be profitable to build much of anything based on an argument from silence in one case. It is safer to look at what we *do* know. If Polycarp had said that the Philippian church did not yet have a bishop, then that would be more informative.