As S. Teodorsson argues in his work on the phonemic system of the Attic dialect, there is evidence that already in the IV century BC, 'popular' Athenian speech underwent changes such as the merger of ι, η, υ in [i]. Even more conservative reconstructions (such as by W.S. Allen) place at least the disappearance of the subscript iota and the monophthongization of οι into [ø:] before 350.
Yet the grammar textbooks by e.g. Dionysius of Halicarnassus often prescribe e.g. the pronunciation of subscript iota as "correct" hundreds of years after its disappearance.
Was that "correct" conservative pronunciation actually used? Did the politicians use different pronunciations in public and in private? Was there perhaps an equivalent of the Transatlantic accent (having artificial archaizing features such as wh = [ʍ]), taught to students of public speaking?
If so, how could e.g. Demosthenes know to pronounce οι as [oi] in speeches and not [ø:] as everyone around him? The Greeks didn't have our methods of linguistic reconstruction, so slowing down natural phonological change seems almost impossible -- and also useless, needlessly alienating the audience of politicians etc.