I would suggest that Becker / Posner doesn't go far enough. To me, we need to call a spade a spade and recognize that the really good players - the Division I players - are going to college for sport, not for knowledge. With that in mind, Division I athletes should be, as Becker / Posner allows, able to collect large sums of money and scholarship for their play. However, we should destroy this false idea that athletes are or should be academics. It boils down to this - college is the pro recruiting ground, and if you can't take the basketball out of the college, you've gotta take the college out of the basketball.
Players should be forced to devote themselves solely to the athletics department - to prepare themselves to specialize in what they probably were going to anyway. Granted, not everyone goes pro from Division I play at college, but those that don't often take careers not far removed (little league coaches!). Colleges of course can still maintain the lower divisions to intermingle with academics - with pay restrictions of course. Think of that as the intramural (for fun) league(s). The average GPA of college sportsmen is atrocious - it's no wonder. Even Butler, the highest GPA in the business is averaging a lowly B.