On the other hand, I suppose it does serve as advertising. Probably a lot more people know of Stanford because of its occasionally excellent football and basketball teams than know of it because of what it has done for computing.
Anyway, that sports and education are so tangled is purely a national oddity of the US, maybe stemming from its tradition of great, and expensive, private universities. During the 19th century, if I recall correctly, it was a sign of distinction and wealth to practice sports; I conjecture that's what got it started in the universities, and then it spread in the early 20th century, when those colleges started courting new talent, intellectual or otherwise, from the up and coming middle classes, helped by the New Deal and the GI Bill.
That could also be why Oxford and Cambridge are relatively so keen on sports, i.e. rowing, as compared to other European universities. Sports were quite the posh thing back then. But, of course, I'm just guessing.
That does not have to be a innate property of education. It's just how science education seems to work, and other education mock science education.
Not saying it's the wrong mode for science education, but.