Yet... that would cease to be the case. You wouldn't be paying for rich people's education. You'd be paying for education for whatever person put in the study time to be a doctor, based on actual merit instead of merit + money. It means that you would have that same chance at schooling. It would mean that doctors could make less money and it probably more likely to live in areas with fewer doctors. And hey, if they become rich, they'll be paying it back into the system and paying for more education that you, as an average-income worker, ever would.

Maybe if you had had free education you could have been a high income guy, perhaps even a doctor!

Once higher education is a public service and not a personal investment, there is much lower returns expected.

Be careful what you wish for, brain drain is a real phenomena.