Your assertion on coherence for a functional society and your extreme hypothetical is fallacious. Multiple governments and societies across the globe operate effectively without a single national language.

The united states for example, current situation acknowledged, saw a meteoric rise even with, perhaps even because of a rich cultural tapestry that could be in no way described as coherent. Sure there are large blocs of cultural identity across multiple regions, but that's about it, and even then that's been on the decline for some time.