Just make the schools free for all, and collect with higher marginal income / wealth taxes.
It should not be dependent on parents’ status either. I got zero aid due to my parents, but I also got zero from my parents.
Although, I also do not think government needs to pay for free schooling for 17 years. Can easily cut some fluff and drop that to 15 years, and still give people a solid foundation equivalent to a Bachelors.