I've read this before, but it's always sort of hand waved (aka I like math and thus far people are like "everyone knows that....") and seems less like something inherent to the role and more like a metabolic deficiency. Not that "herbivores don't need to be smart" and "herbivores can't afford to be smart" are contradictory.
It looks like there was
actually a recent study about wether human brains are unusually energy-hungry.
A: Nope, they aren't. We devote about as much of our daily energy budget to our brains as many others in our clade, including tree shrews.
Further examination of the claim that we have unusually large brains shows that our brains are not unusually large among animals: the actual claim is more nuanced, which is that our brains are unusually large
for an animal of our body weight.
So the answer, as is usual with science, gets more complex the more you investigate it. Widely-applicable models like the Theory of Evolution or Theory of Gravity are remarkable because they are rare.
Reading between the lines here and hypothesizing: Brain size scales with body size because larger bodies mean more sensorimotor signals to process. Encephalization quotient, then,
might be a proxy for how much of the brain isn't dedicated to "signals processing", which itself
might be a proxy for intelligence. These relationships appear to hold for mammals, so this model accurately predicts that dolphins are relatively intelligent animals.
However, avians and reptiles have very different brain structure from mammals, so this double-indirect proxy doesn't accurately predict their intelligence levels. Some hypotheses:
1: Brains in general can get smarter without getting larger, but this has only been selected for in avians.
2: Bird brains' neuroanatomy gives
them specifically the ability to get smarter without getting larger.
3: The scale factor for avian brain sizes is different, and therefore a mammal baseline gives bad results.
Examining the animals outlined in the study, it looks like the other comparable extant mammals are
much smaller than us, and therefore their brain's energy expenditure is unsurprising. They have a similar brain-to-body-size ratio to us, but because they are much smaller, a much greater portion of that brain mass has to be devoted to the autonomous nervous system.
So then this ought to predict that humans have unusually fast metabolisms for a large animal. (Googling now...)
...
and indeed this is the case.
So to summarize:
Compared to all other mammals:
1: Humans have slow metabolisms, as expected for a large animal.
2: Humans have slightly-above-average brain size, but don't stand out.
3: Humans don't use an unusually large portion of our daily energy budget on our brains.
4: Humans are unusually large - in the top quarter of all species.
Compared to other mammals
of a similar body size:
1: Humans have unusually fast metabolisms.
2: Humans have
astonishingly big brains. (Encephalization quotient of ~7.5: the same calculation produces a value of ~4.5 for dolphins and a value of ~2.5 for chimps, orcas and elephants.)
3: We don't know for sure if we use an unusually large portion of our daily energy budget on our brains, but I would
expect the answer to be "yes."
My personal conclusion:
Humans are unusual in that they've preserved the brain-to-body-size ratio, metabolic rate, and percentage energy expenditure of the brain of a much smaller animal. None of this is unprecedented: what's weird about us is that we've retained these traits that other species lose as they grow bigger.
This suggests that there's selection pressure against higher metabolic rate and higher proportion of energy spent on the brain in megafauna, which makes sense when you consider the relative strength of a human vs. e. g. a chimpanzee. In a bare-knuckle match between a modern human and a chimpanzee, I'd bet on the chimp.
However, these traits have reason to exist, because they're adaptive when you're a tiny little tree shrew. You need all that brain just to manage your senses and reflexes. You also need that high metabolic rate so you can
explode into action when you're about to be eaten by a predator.
So this results in the surprising conclusion that the human brain
might be an atavistic trait! Far from being "more evolved" than other species, the secrets of intelligence might rest in a very small shrew-like creature we happened to retain some genetic code from.