that's a good point. They are tightly integrated into the college whose charter is to educate. whereas a pro team will take anyone for the express purpose of the performing the sport well.

Further, colleges receive public money but are not free to attend for most students. And I am not talking about "free" from the students perspective, I mean most would not be permitted to enroll if significant tuition dollars were not deposited (unlike public schools, for instance). Also, plenty of colleges are private but have NCAA teams.