I'm not sure, but I think your model assumes intelligence is mostly (entirely?) useful for males. Actually, females also have a complex bunch of roles, since they need to take care of themselves and their children and make alliances to get help from both males and females.
You might be interested in Mother Nature by Sarah Hrdy.
Actually it is notable that women and men have such similar intelligence. Women and men are quite easy to distinguish physically in a variety of ways, but there is probably way ( I don't believe one has been discovered) to reliably distinguish a woman from a man based purely on how their minds work. Minds are a lot more like livers, kidneys and eyeballs (effectively identical in each sex) than like body shape, genitals or hair distribution. I haven't heard this said before, but this would seem to suggest that minds are NOT primarily to get us laid, that they do not evolve from sexual selection, but rather arise from natural selection (survival of the fittest).
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