> If bigger brains lead to higher intelligence, why do many highly intelligent people have average-sized heads?
There IS a correlation between intelligence and brain size (of about 0.3). But the human brain does a lot of things apart from what we measure as "IQ". What shows up in IQ tests tend to be mostly related to variation of the thickness of certain areas of the cortex [1].
The rest of the brain is, however, responsible from a lot of the functions that separates GPT-4 or Tesla's self driving from a human. Those are things we tend to take for granted in healthy humans, or that can show up as talents we don't think of as "intelligence".
Also, the variation in the size of human brains is relatively small, so the specifics of how a given brain is organized probably contributes to more of the total variance than absolute size.
That being said, a chimp brain is not likely to produce (adult, healthy) human level intelligence.
> And do they need to eat much more to fuel their high IQs?
That depends on the size of the brain, primarily. Human brains consume significantly more calories than a chimp brains.
> If larger brains were always better, wouldn’t female hips have evolved to accommodate them?
They did, and significantly so. In particular the part around the birth canal.
> I think human IQ might be where it is because extremely high intelligence vs. what we on average have now) often leads to fewer descendants. Less awareness of reality can lead to more "reproductive bliss."
I believe this is more of a modern phenomenon, mostly affecting women from the 20th century on. There may have been similar situations at times in the past, too. But generally, over the last several million years, human intelligence has been rising sharply.
[1] https://www.sciencedirect.com/science/article/abs/pii/S03064....