That really isn't true. The NCAA never came up with a system to deal with NIL. I mean unless you consider we aren't allowing any of it to be dealing with it. Which was absurd, and why they lost in court.
What athletes gain as employees is protections that all other employees have. To start with, a paycheck. Seems like a lot of athletes might like that, since most college athletes don't actually make money on things like NIL. And they would get health insurance, which they do not currently get. They would get protections so that if they were injured playing and practicing their sports that the University can't just simply cut them loose, like they can now, the schools would have to pay for all the medical care needed until the problem was solved. It would also give the athletes a chance to organize into a union and ask for and possibly get things that the schools don't do right now. For instance they could make scholarships guaranteed for four or five years. They could try to get guarantees that if athletes had to leave school before finishing their degree that they could come back at a later date and finish their education. And whatever else they might dream up.
Seriously, I can't think of any reason why an athlete wouldn't prefer to be considered an employee. What would the real world downside be?