The universities are NOT employed by the NCAA. Neither are the students. The NCAA is a governing body over the athletic programs associated with the universities, just like the TSSAA has oversight over high school athletic programs in the state of Tennessee.
The NCAA is trying to do what they were charged to do - set guidelines under which all universities operate so that all of them have the same chance to succeed. Without a governing body there are no rules - it would truly be the wild west and lawsuits would definitely happen when women's sports are removed, just because they would prevent money from going to support the payment to football players. And schools could play players of any age, as many years as the player wanted to play, regardless of whether they attended school or not.
Greed will ultimately destroy athletics as we know it at the college level.
The problem with NIL is that it is being abused and is not what it was intended to be. It has become a loophole used to promise money to a player to attend a specific school.