Another reader joins the discussion:
The biggest obstacle to paying college athletes is U.S. tax law and a century-old designation. As your earlier reader noted, American universities are non-profits. This does not mean they pay no taxes, just that they avoid taxes on any income related to their charitable mission. So, for instance, they pay Unrelated Business Income Tax on the sale of t-shirts in their student stores. College athletics is a multi-billion dollar industry, and universities avoid taxation on that income by a long-held designation of athletics as part of the educational experience given to their students.
This was first made back at the first inception of the NCAA in the early 20th century, and will be difficult to overturn based on that historical inertia. As a result, and to conform with non-profit tax law, student-athletes cannot receive any benefits that non-athletes don't also receive. To receive even a single dollar in excess would impute that it was in exchange for a service above and not part of the educational experience, i.e. the student-athlete was paid for being an athlete. This jeopardizes not only the tax status of the member institution for whom the athlete pays, but the non-profit status of all universities (which is why the NCAA appears to come down so hard on even relatively minor violations of their rules regarding "extra benefits").
The easiest solution is to declare college athletics to no longer be part of the educational experience. Under that scenario, colleges would be free to pay athletes – just as they would pay students who provide other services to the school such as tutors and cashiers. Plus, they would not have to worry about Title IX compliance in regards to athletics, which every school with a football program is technically in violation of.
The downside would be those same schools having to pay much more in taxes, some in amounts measured in millions, and paying athletes would increase the costs associated with sports programs. And that's also the reason why the NCAA member schools will never willingly go for it.
The IRS could fix this anytime it wants, but there are too many political pressures against them doing so as well. So instead we are left with a sports industry with clearly identifiable professional athletes and a conflagration of laws and political and historical pressures that deny those athletes professional status. It is a situation that passed bizarre and entered absurdity several decades ago.