Problem is if you make them pay their own tuition, you are straight up putting all private schools at a huge disadvantage, just like it has been done in baseball. Kids would say, "I could pay $50k to go to a private school, $25kto go to an out of state school, or $10-15k to go to an in-state school." It would be a major advantage for UF, FSU, UCF in Florida. Coaches and ADs would push back because they want to go after out of state talent and not have a disadvantage.
You either keep covering scholarships or you subtract all scholarships of all the conference schools from the media deal (like any business would deduct a legit business expense) and then divide the net.