Some things concerning the student focusing on pronunciation, perfect grammar, idioms, and other techniques to develop a stylish mode of speech:
(1) Speaking perfectly is not linguistically possible to accomplish below the mastery level.
That means in the student dedicated to elocution you get a speaker whose pronunciation, grammar and style are polished and interesting -- but they can't understand what any other speaker of English is saying. They have spent a lot of time commiting grammatical paradigms to memory, so they can ask a very adroit question -- nevertheless, they have developed no skills going toward understanding the question's answer.
(2) Adherents of the Grammar-Translation Method of language instruction are often habituated to elocution as well.
(3) Studying language from a grammar -- or, for that matter, elocution -- point of view can form learning blocks.