Should student athletes be employees of the University they play for

[cheermomtoo]

Colleges make a lot of money with their football and basketball programs.  I saw a discussion on TV that athletes feel that they make a lot of money for the college they play for but don't benefit from it.  Their opinion was that they should be paid employees of the university, have benefits, insurance and worker's comp for injuries.  They also wanted to have a say in how the profits are spent.  If the football program brought in $5 million, they didn't want the University to have the power to allocate part of it to the music dept, library, etc.  They wanted the power to decide.
I thought they benefited with a scholarship, education, and exposure to scouts and the chance to move into the professional arena.  Do you think student athletes should unionize to become employees of the universities they play for ?