But yeah for early game, it seems like a simple solution, and the answer is proper delegation instead of a free-for-all.

That's the problem. Humans would each gravitate to what they do best and organise themselves into a structure relatively quickly.

LLMs get stuck in circular patterns because they don't have the ability to do that. They can't think outside the box. None of them arbitrarily becomes the boss to take charge. They're all yes men stuck in endless board meetings where even just flipping a coin would break the deadlock. But they are incapable of realising that, because they are just statistical regurgitation machines flavoured with a bit of randomness on the most probable outputs.