Certainly driven by the need for more complex education than merely imitating one's elders.
A grunt meaning "hit" is fine for cracking nuts, but one needs loads of grunts to indicate "hit hard", "hit sideways", "hit glancing", "lots of little hits", etc. Eventually, one needs more modulated grunts - bingo! Language begins.

I have a high regard for Chomsky, but he’s not always right, and has been known to reverse his position.

I'd be interested to see if the NOTCH21 gene mutation on chromosome 1 matches up dates with this because that could be the threshold for our intellectual evolution.

Not from the first grunts and groans? Especially those of the dominant individuals?