Rights? Rights to what? To make money off their likeness? They don't lose that right. They still have the right to do it. They just can't do it while playing college sports. You sign a thing that says you can't or they kick you out or suspend you. You sign it, you agree to it. Don't agree? Don't sign it. Or sign it and then go on a strategic strike that brings the system to a halt.
People make these choices all the time. If I work at one paper, I lose the ability to work for the competitor unless I leave my current employer.
While far different in degree, it's not different in kind.
College athletes can always choose to strike. Just not play. In fact, I think it'd be good if they did. Then we'd have the standoff we need to have, the NCAA would or wouldn't respond with replacement players, and away we'd go.
What instead has happened - and we think it's a good thing but, in many ways, it really isn't - is a constant media shaming campaign to change things. Seems like the right thing to do, probably isn't, and what's one person's "righteous" media campaign - say, the crusade against liberalism in America - is another person's blight on humanity.
It's what liberals either don't understand or have stopped understanding or choose not to understand. Advocacy journalism goes both ways. Conservatives and traditionalists aren't just going to sit it out while all the "better, smarter" people solve all the world's problems, including college athlete compensation.
(And, yes, there are conservatives who think college athletes should be able to make money off their likeness.)