I think they should be on a college team.
I think they should be going to college.
I do not think they should be paid.
Like most people, they are preparing for their future in the field of their interest.
The issue, in my opinion, is that we attempt to shoehorn them into "traditional" curriculum. They're forced to choose a major, often funneled into the easiest thing just to get through.
Fundamentally, the majority are in college to learn and prepare for life as a professional athlete (assuming we're talking about the "Big 3" sports). Let's allow them to do that. Let's provide programs that focus on that, that teach sport fundamentals, dealing with the media, managing money, dealing with agents, fundamentals of business, etc. Let's also provide routes for post-professional-sport life, like lower-level media classes, etc.
We seem to have an aversion to treating a lucrative and very real profession like something that warrants education.
Edit: The problem with $ and athletes largely applies solely to football, wherein the NCAA and NFL have colluded to force high school talent to play somewhere for three years after graduation. This is arbitrary and stupid, and forces kids into programs they don't care about, for institutions that they don't care about. This is the primary issue with not paying players. It's not that colleges don't pay, it's that there's no other opportunity to get paid.