How are college sports teams not government sports teams?

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.

If you search YouTube for "fail army" there is clearly a whole ad supported business model for revenue from something that is about the same as "ow, my balls!"

This is basically https://chive.tv