[Pelam]

IANAB, but large animal bodies correlate with large brain size. Huge animals like elephants and whales have much bigger brains than humans, but are not considered cognitively equivalent to humans.

Maybe moving and maintaining a body requires body size proportional "raw" computational power and maybe human brains have mostly just qualitative differences not related to mass when compared to animals (ok, and a bit of extra proportional brain mass too).

If this is the case the connection between excercise and cognitive capacity could seem natural. Excercise requires massive neural resources and thus physical excercises also excercise the brain to a large degree and the whatever qualitative bit that humans have "on top" simply rides the wave to some improvement.