Paid for playing? No. Their payment comes in the form of athletic scholarships and a 'degree' they didn't really earn.
What they should be allowed to do, however, is make money off of endorsements and the like. They should ABSOLUTELY have control over, and be compensated for, their likeness. NCAA video games, marketing campaigns, all of that.
FFRK: BRKB - Eiko - Guardian Mog
FFBE: 885,063,087 - Orlandeau - 931 ATK