Why is the choice framed as "make all of them give up the free education. . . . ." in exchange for a relative handful getting big money?
I would suggest that the BASELINE owed (analogous to minimum wage) is the present setup; to those relative handful who could (by dint of their superior skills in a superior skills environment) earn more, well, that's a reward for hard, hard work.
Note that over the years since the present basic scholly structure evolved, the $$$$$$ have dramatically increased and schools, coaches, and the NCAA rake in fortunes - but players haven't fundamentally increased their well being. This allows the very best - upon whose skills others make fortunes - to get theirs (and not at the expense of the many). To the rest - the vast majority - they get what they've been getting (earned through their hard, hard work).
As problems arise under this change, adjustments will need to be made - just like under the present scheme.