Sports demand real cognition, not less than philosophy, arguably more, since it happens live, under time pressure, with a body that must execute the conclusion instantly. A point guard reading a defense while the shot clock runs down is doing applied game theory. A boxer managing distance is running live Bayesian updates on an opponent's intent every half-second. "Think with your muscles" gets it backwards: muscles are just the output device: what's upstream is pattern recognition and split-second reasoning under uncertainty, the kind philosophers usually get to do slowly, with a pen and no clock.

As for competition being some corrupted, zero-sum betrayal of philosophy's higher aims, Nietzsche would say you have it exactly backwards. He didn't see struggle as an unfortunate feature of life to be reasoned away; he saw it as life's basic structure. "Life is will to power," and where there's no resistance to overcome, there's no growth. "What does not kill me makes me stronger" wasn't a locker-room slogan to him, it was near his actual metaphysics.

He also admired the Greek agon, the competitive contest underlying their tragedy, philosophy, and athletics alike. In "Homer's Contest" he argued the Greeks needed structured competition to keep ambition from curdling into destruction, the contest channels will to power into something generative rather than annihilating. Sport isn't philosophy's opposite; it's an old technology for making competition survivable, even beautiful.

So framing this as philosophy-versus-sports, which wins, may be the more "neanderthal" move, it smuggles in the same zero-sum, must-crown-a-victor logic you're accusing sports fans of, just relocated to the seminar room. Nietzsche's real challenge wasn't ranking pursuits; it was asking why you need a hierarchy at all, rather than seeing both as arenas where the same drive, to test yourself against resistance and become more, gets expressed.