Another reason given for why human intelligence must be simple, is that we've only had time for a few complex evolutionary adaptations since we split off from other primates. Chimps clearly aren't particularly adapted to, say, doing math, so our ability to do math must come from a combination of some kind of General Intelligence, which can be applied to all kinds of tasks (what Eliezer called "the master trick"), and maybe a few specific adaptations.

I don't think we should assume that the vast difference between human and primate achievement is caused by a vast difference in human and primate general intelligence. There are vast differences in achievement between human groups, but only fairly modest intelligence differences. Some ape experts estimated the IQ of chimps as above 75.

Chimps have been known to use some surprisingly advanced technologies, almost comparable to the more primitive human groups (like Tasmanian Aborigines). Sometimes, chimps notice other chimps doing these things and copy them, but they don't teach these new techniques to each other in any comprehensive way. This strikes me as the main advantage humans have, rather than raw mental firepower.

It seems likely to me that the main biological adaptation that made humans so much more successful at learning was not general intelligence, but rather a more advanced theory of mind and communication skills that followed from it. I'm sure general intelligence improvements played a role, but my guess is g was secondary to social learning.