I was under the impression - not having studied much about Jaynes' theory - that it is a well-regarded but falsified theory. That being said, what you describe sounds like an amazing premise for a novel.
Voices plural? I doubt most of society experiences such a phenomenon, and if they do they’re not talking about it.
The other more phenomenological aspects are not easily falsifiable, nor indeed verifiable. But the arguments he provides at least itch the scratch of explaining strange behaviors and characteristics of our ancestors and the relics they left behind in a way that approaches Occam's razor.