I've told this story before, but I lived with one of my best friends from high school and in college at Marquette.
His parents (janitor, school secretary) made about 50K combined, and he was on a partial golf scholarship at a school with high tuition...
He was never poor and never worked a day in college. He took out loans because he wanted to, but he didn't have to. He graduated ~ 12K in debt and lived very comfortably.
Living with him, I realized the NCAA takes care of the athletes better than most people think. For instance, he lost his iphone one time, filed a paper to NCAA, and was sent a check for $450 to replace his cell phone, no questions asked. Think about that for a second... An iphone, replaced, by the NCAA. The NCAA has PLENTY of emergency funds available, even to golfers...
These horror stories you hear about are an examples of a person spending their money in really ridiculous ways, but we don't hear about what stupid 'toys' they bought, only that they've ran out of cash for 'meals'.
Paying the athletes would further segregate students from athletes. At big time schools, they're already treated differently, idolized and despised by the other students, and giving them more money and power just strengthens that.
Offer them financial advice rather than more cash. College is about learning to live in frugality so you can appreciate the spoils your hard work gives you afterwards, not for living wealthy while you're 20 and are obsessed with yourself and nice things and spending $25 a day on food.