Let me clarify -- why is this allowed? Colleges have shitloads of government funding and regulation behind them, why are they allowed to engage in business that is clearly at odds with their primary purpose? And if sports are OK then why not, say, strip clubs?
Money. Just like everything else.
Football brings in multiple tens of millions of dollars per year in income (after expenses) at traditional football powers. A total of over $1 billion this year amongst all schools.
Strip clubs, not so much cash, and worse yet, they might turn off alumni donors.
Also football is NOT "clearly at odds with the primary purpose" of a university. It's an entertainment function for students and alumni, and there are careers in the industry for which the university is preparing students. If you ban football, you better kick out all the Drama majors, Fine Arts majors, literature majors, and fuck just about everything else that wasn't hard science, business, or engineering. You could call it... Purdue.