alt Hacker News> I can't prove, but strongly suspect that this is the case.
I think you can benefit from reading Franz de Waal works. He was a primatologist and he had a similar ideas. Though according to him intelligence was (is) not just a useless "peacock feather", he adds one more block in your feedback loop: hierarchy. Intelligence is used by males to play political games to raise their social status. Social status influences frequency of reproduction for males, so there is a natural (?) selection for political success which depends on good looks, physical fitness and intelligence.
It works for a lot of species but higher primates somehow got enough intelligence to make it dominate good looks and physical fitness and then the positive feedback loop led to evolution of Homo Sapience.
I especially like this theory because it explain why people lose all their pretense to be rational when it comes to politics: human mind is political first. Language, logic, rational discourse are later inventions on top of a political mind. They can work in a neutral environment but when it comes to politics Nature gets the upper hand, and the cultural intellectual sediments of rational thought are wiped instantly, and people's intelligence drops to levels of chimpanzee's: keep alliance with the strongest alpha if you can, rational discourse be damned. One needs a very strong mental discipline to resist it.
> Humans become more intelligent on the scale of mere millenia because more intelligence does improve the judgement of the females.
This idea doesn't explain how intelligence became so important for females. Your idea is like chicken-and-egg problem, you can explain how chickens and eggs let each other to exist, but not where did the first chicked (or egg) come from. And the idea relies on the assumption that female's opinion matters. It matters for some species and doesn't matter for others. It matters in some societies and doesn't matter in others.
> It is well established that evolution is driven not only by fitness in the trivial sense of "survival or death", but in large part by mate selection.
When I read this I thought you'd go about role of sexual dimorphism in evolution and Vigen Geodakyan evolutionary theory of sex[1], but no. Still you may be interested, though I want to note, I don't know if the theory is "scientific" or not. I'm not a biologist to judge, and I didn't have luck to find some kind of a scientific debate about it. Some objections to the theory, but not full-blown attempts to dismantle it. And I think the theory is not politically correct: it implies that roles of males and females in evolution are different. It is not bad per se, but you know how (most of) people think (with their political mind borrowed from chimpanzee): if roles are different in evolution, then you can argue for a society change that would mirror it and would give you some privileges and raise your social status against some others, and then you would get new kind of Nazis trying to genocide half the population of Homo Sapience.