Couldn't they simply not give them scholarships, have them be preferred walk-ons, and siphon some money to "tuition" payments?
Seems like there's already a workaround or two.

5-6+ deep on all of the position slots. There would have to be one hell of a NIL to keep the guys who aren't likely to crack the 2 deep. Maybe, maybe a few elite schools/coaches can convince guys to remain in the "system" for a chance to play for a championship/draft slot senior year. The transfer portal will see a lot of disgruntled players, with fewer options of places to go if most teams have an overstuffed depth chart. FCS and D2/D3 schools might have a harder time getting recruits out of high school, but they might have an avenue for filling out a very competitive roster filled with transfers.

for two reasons.

1) As you suggest, I don't think there's too many more players that schools could keep around; but

2) Even if they are, is it really a bad thing if there's more kids on scholarship at school?

The change I'd like to see is making scholarships be guaranteed renewable at the option of the athlete.