Any other student wouldn't have the university taking a cut of what they earned using their own name or image.
Are you saying that in order to profit from their likeness, they have to give a percentage to the university?
Regardless, from a tax standpoint, they should be taxed on earnings they get from their likeness, name, image, etc. They should be taxed on scholarships amounts that go towards things other than tuition, fees and books. They should not be taxed on scholarship amounts that go towards tuition, fees and books. This is how it is for any other student.
No what I'm saying is that under the model that's likely to be used, most of what students will get through NIL will be filtered through the universities because players don't/won't have licensing rights. Apparel and memorabilia will be sold thought the schools licensing deal, meaning the players won't have control over how they are licenced or what their cut is. The universities would be getting the money and simply giving the players the cut they deserve. In this instance the university would be taxed, not the player, not unless you think double taxes should be applied to the same cut of money.
If the player uses NIL to give lessons then they would be an independent contactor, and would be taxed as much as they are willing to pay, identical to the student getting paid to tutor a middle school algebra student.
A player getting paid for an endorsement, like the independent contactor, would be responsible for paying their own taxes on what they earn. An endorser isn't paid and taxed like an employee because they aren't an employee.
So to wrap this up, to do what LN proposed would require the country to change its tax code, to the detriment of anyone who is an independent contactor.