If given the chance to design an educational system from scratch, including the laws that govern and affect education, no one, except perhaps some percentage of those who have become habituated to working in the current system, would design one anything like what we have now. For both public and private schools, the goals would not be the same, and the means for trying to achieve them would not be the same.
Schooling has essentially, though probably not intentionally, become the efficient warehousing of children in a way convenient to society at the expense of many teachers, virtually all students (with a certain kind of exception(1)), and at great opportunity costs for society itself. It is not that there are no "effective" schools in the sense of turning out students who can go on to function in various careers and social roles; it is that even the schools that are effective in this way, are effective at great costs to students and at great opportunity costs to society. Many (young) people could learn far more that would be far more useful to them and to society if education were different. The ever increasing number of years children are required to attend school, basically doing assignments that have no meaning to them and little relevance to socially useful work, serves to postpone children's maturation rather than giving them more opportunity to learn and to develop discerning judgment. Children learn to read and write by the fifth or sixth grade, but are not given the opportunities to hone or apply those skills in either useful or interesting areas. Instead the best students simply become good at doing things which are primarily only useful and rewarded in school itself.
Schools have taken on a life of their own that has little to do with the needs of society, children, or the adults those children will become. The worst students who are forced to stay in school, do so as prisoners remain in jail, developing all the same sorts of unhealthy and unproductive, or even destructive attitudes and characteristics. The best students end their senior years in high school, and often their senior years in college, unable to grow anything, make anything, build anything, or repair anything unless they learned to do those things outside of school. They have little understanding of human nature or its higher potentials. They cannot even imagine, let alone appreciate, the potential non-material richness of life or the capacity of the human spirit. They cannot analyze situations or problems into components from which they can draw insights. They cannot discover, or even see when it is pointed out to them, lessons for their own lives in history, literature, or science. They cannot discover lessons even in their own circumstances because they have not learned to see their circumstances objectively. They cannot compare their circumstances with those of other cultures or times. They cannot make appropriate, useful distinctions. For the most part they cannot think about anything in other than a superficial or mechanical way. At best they can write useless papers or do useless projects in ways no one cares about, on topics that have no excitement or meaning for anyone, including themselves.
College teachers and employers alike are unhappy with the quality and the level of immaturity of students that K-12 schools produce. I don't believe that is because schools don't have the resources to do what they want to do with students -- though they often do not have the resources they need or would like - but it is because they do, and want to do, the wrong things with children. If schools had greater resources and more time with students, they would, I think, produce even less educated students in greater quantities - better "schooled", but less educated. Schools are not places that inspire children to want to learn and think while giving them the tools and opportunities to do so; they are not places that give children meaningful responsibility in order to produce conscientious, mature adults and citizens. They are places where obedient children learn to do what they are told or learn to do what teachers will reward, and where independent or defiant children learn to (further) despise mere authority and often to confuse it with deserved leadership.
Basically students are taught facts they will forget before they ever become useful, except on exams, to themselves or anyone. Much of the subject matter in schools is of no significance to adults, and the school subject matter which might be of use and interest to adults, is not taught in a way that is very meaningful or helpful to children. Students are taught grammar and trivialized rules of composition, instead of being taught how to communicate clearly and effectively, which is a very different thing. While grammar and composition are important elements of clear and effective writing and speaking, they are not substitutes for them, and they are often not tools for achieving them. Superficial thinking about trivial topics, or about trivialized aspects of important topics, is what is fostered in schools, rather than deeper reflection about significant elements in life. Science and math, literature and social studies are taught in ways which have little meaning or relevance to students, often by teachers who aren't particularly expert in that subject matter content area, or anything else other than what is the latest pedagogical fashion; students are basically graded on how well they can remember mere statements of THE SYSTEM!