This same point was also made clumsily in the OP; I’m very unconvinced.

The obvious question marks in that theory:

Lots of human labor happens in nondemocratic polities; slave-owning/repressive societies create lots of labor.

Democracy historically doesn’t advance in lockstep with labor; it’s arisen with many contingencies. The model (English Parliament) seems founded on concerns with right of some wealthy barons v. Kings.

Traditional common sense alternative is that military victory goes to people with largest army, so voting saves time. That’s been debatably less relevant with deadlier weapons, so democracy could be cooked.

I don't think it is required, democracies aren't designed that way

not everyone in charge is a cartoon villain