Well a.) I’m arguing how it should work (not how it currently does) and b.) why your Cola metaphor doesn’t really make sense because Coke vs Pepsi isn’t the equivalent of Notre Dame vs Iowa State.That's up to the players. They can't be forced to form a union. Until one exists, employment laws and the Sherman Antitrust act applies.
Also, there is an injunction on the FTC’s non-compete ban so schools could potentially offer contracts (if they classified them as employees) with non-competes or at least penalties if they leave. Now if every school did that would they be guilty of collusion. Probably, but I don’t know, that would be up to the courts. Or if the NCAA gets anti-trust exemption then they could potentially go that route too.