At least in some cases, that would likely have the effect of making college education less accessible to poorer people. The richer people are currently subsidizing the poorer people; if you disallow that and have everyone pay the average, the richer students would pay less, but the poorer students would be priced out entirely. I think that would end up being a net negative for society.

(I agree the U.S. university pricing system as it stands is far from perfect.)