Yes, they would.
If you are in higher ed, you know one of the major issues is tuition billing. Students have been very active across the country in making sure their tuition bills are itemized so they know specifically what they are paying for and where their money is going. Students are fighting back on junk fees with tuition and on obscure things on the bill in which they don't know what it is or where, specifically, that money is going.
If students find out their tuition is eventually going to pay for the football player who sits next to them in class, then that will cause an uproar.
As far a laws as to what student athletic fees can be used for, that is on an institution by institution basis. Larger P5 institutions have optional fees like UT where you pay for it if you want and it gives you access. As long as it's optional, it's fine because students know what they are signing up for. You can't just backdoor it on to tuition for all students.