I mean, most settings do that. FR has dozens of languages, so does Darksun. In my setting 'common' is the language of a single island nation that is used by most human merchants and many sailors, and well travelled people tend to pick it up eventually.

I suspect there is less variability linguistically than we see in the real world though. Very long lived races would keep the drift more static, and immortal beings (including the Gods) may have an interest in keeping things 'right'. That, coupled with the 'etched unerringly into the bones of the cosmos' planar languages would work to slow linguistic diversity.

In fact, sometimes I wonder why we have some of the languages we do in the first place. Why is there Elven when Sylvan exists (and every pixie that springs into life at the sound of a child's laughter knows it)? It almost has to be a constructed language; one that started as a secret code or something that developed into a full language later; or something the Gods encouraged to separate the elves from their Fey roots or something.