While you have brought no evidence to suggest that it shouldn't be allowed (I believe there is quite a bit, although it's outside the scope of this answer), that's not what happened.
Changes in language occur organically. Compare, for example, Cockney English to the Queen's English to standard American English (and even the latter to Appalachian English).
In the 7th chapter of Bava Kama (Bab. 83a) the Gemara quotes a Baraitha that mentions the language of "Sursi", and there is a commentary by Tosafoth explaining that "Sursi" is a dialect of Aramaic spoken in Eretz Yisrael. To address the obvious question of why it has a different name, Rabbeinu Tam says: "לפי שמעט משתנה כעין לשון לעז שמדברים אותו לשון צח במדינה אחת יותר מבאחרת"; (loose translation) "It had changed enough to be considered its own language, similar to La'az, which is more or less pure depending on where you are."
I've personally always found that statement fascinating, when you consider that now, though Romance languages share similarities, they are regarded as entirely distinct. Evidently, in the 12th Century or so, they were still close enough that the relationship between them could be used as an example to explain this phenomenon happening to Aramaic in Eretz Yisrael in the times of Tannaim.*
Different regions and groups have developed different pronunciations for the same words, and each claims Mesorah for its organic development, and any prohibition that may exist against changing one's pronunciation is against changing outside of one's tradition to a different one or a new one.
* Charles Koppelman points out that I may have made too great an assumption that La'az refers to Romance languages as they were evolving in the 12th Century, and that it may refer to French itself as it was evolving. I wouldn't say I'm convinced, but he makes a good argument. In either case, the point is that it demonstrates that languages do evolve organically, especially when regional divisions are considered.