Do they get to take advantage of labor laws protecting organizing since they're not actually, like, employed? Obviously the minimum wage doesn't apply to them...
If they don't have the protection, doing that could jeopardize any chance they have of going to the NFL (not that most of them make it anyways).
Student athletes' biggest protection from retaliation is probably their incredible power over the institution and high level of visibility, as demonstrated by the actions of the Mizzou players during #concernedstudent1950.
Football players, at least in D1, have also been determined to at least have some of the rights to concerted action protected under the NLRA:
Of course, while that does protect them from their current employer (the school), I don't think it can protect them against the reluctance of a potential future employer (like the NFL).
It's a similar situation, but there are even less professional jobs, less alternatives after graduation, and a n increased risk for injury.