These guys DO go through a course from the NFL on managing money, etc. The NFL is actually pretty concerned about it, as it should be.
Purely from a public relations point of view, if nothing else. I remember when I was in high school, Joe Namath signed with the Jets, and part of his package was a $100 dollar a week life annuity. I remember a classmate saying, "Think about it, he can never be a poor man,"
They could introduce a league rule (with the cooperation of the union) requiring a certain percentage of the players' income be in the form of deferred compensation, i.e., a pension. (Doesn't MLB have a pension program?)
The NFL minimum salary is $420,000/season. Even if 25% were in deferred compensation ($105k), a 6% annuity would only yield $6300/yr, not enough for health insurance. Still, no one should expect the NFL to support every one who ever played one season for the rest of their natural life.
I think I remember Dave Ramsey saying he was involved in this.