That presumes that languages didn't evolve independently across different communities. The fact that different ancient languages have completely different grammatical structures, for example, provides some evidence of this.

> The fact that different ancient languages have completely different grammatical structures, for example, provides some evidence of this

It really doesn't provide that evidence. Proto-Afroasiatic the oldest agreed upon hypothetical proto-language probably only dates back 18,000 years. The modern brain, vocal, and tongue structures linked to complex speech were in place 100,000 years ago, and its thought that complex speech was in place by the time Homo Sapiens left Africa 50-70,000 years ago. That's a long time for grammar to diverge. Just in recorded history plenty of languages have gained and lost very complex grammatical features. Old Chinese for example was not a tonal language, but evolved tones. Small isolated languages can change rapidly, and trade languages tend to simplify.