"What seems to have worked best for cultures is to play off the men against each other, competing for respect and other rewards that end up distributed very unequally. Men have to prove themselves by producing things the society values."
I'm not sure that men's willingness to make things that people want really sets them apart from women. Across cultures, women play an important (and often exclusive) role in the economy -- drying fish or tending sheep or what have you.
Women rarely played a role in the macro-economy, true enough; but for much of history, trade within a village was for more valuable than trade between villages or nations. It's misleading to suggest that the present worthlessness of small scale trade implies the past worthlessness of women as economic engines.
