Theoretically, it is fixable.
1. Require student athletes to report all their NIL deals to the schools compliance officer. Failure to report a deal is grounds for loss of eligibility.
2. Cap the amount of NIL which is allowable under NCAA rules. Note that you are not restricting what an individual can earn from his or her name image or likeness, you are just restricting the amount that an individual can earn and still be considered eligible for participation as a student athlete at NCAA institutions.
3. Require that payments be individual based in not institution based. This would illuminate the current practice of offering every member of a football team the use of a car, or offering every offensive lineman $10,000.
4. Require that any payments be actually linked to the use of name image or likeness in a marketing campaign.
That wouldn't eliminate all the abuse, but the system would immediately become less prone to abuse.
The thing is, I had the NCAA stepped up at the start of this they probably could've kept NIL payments at some reasonable dollar amount, say $15,000 or $20,000. Now that a cottage industry has been created, it will be incredibly hard to roll back the existing system.
The notion that the NCAA somehow needs federal action to fix this is a fallacy. It is a private organization and can set its rules for membership as it sees fit, provided that those rules don't violate federal or local law.