This isn’t a black and white case where “proofs” exist. Indian history is notoriously hard to study due to lack of primary sources.

> historical changes in Sanskrit used in the Vedas.

This is just one small corpus of Sanskrit linguistic traditions. It hardly gives them expertise over the rest of the traditions spanning few millennia.

Jains, Buddhists and various other Sramana movements were championed by lower varnas and they all used Sanskrit as a liturgical language.

I have already mentioned the widespread presence of edicts, danapatra, inscriptions, secular literature created for wider public which hints that Sanskrit was widely understood and Sanskrit/Prakrit Diglossia is not too far fetched.