Yes, some universities are millionaires. Those are the ones recognized worldwide as the best places on earth to get an education. They already fund whoever they want to add to their alumni rolls. Government meddling isn't going to improve their situations. But sure, they may be some that an unconstitutional federal takeover would improve. I mean, Bernie Sanders claims to know a lot about education. Let's ask the students of Burlington College how happy they are that his wife took over....
The idea that free education means lots more people will get higher paying jobs is unproven at best, and a red herring at worst. The President was right to call for more vocational training in every US High School. And unless the government dictates what people study, the slackers who are hiding from real life by going to college (I met several who were doing it on Mommy and Daddy's dime - there'd be millions more if they never had to tell a relative what they were "studying.") are going to be majoring in the cultural history of television. All they'll be raking in after graduation are crumbs off of table 42.
Power corrupts, and absolute power corrupts absolutely. The federal bureaucrats who'd run this program would be fleecing and abusing their positions within minutes. And the Soviet Union had free college. Who had better aircraft, computers, etc.? The "give it out for free" crowd, or us capitalists?
Nationalizing is inefficient in small countries, and disastrous in larger ones.