Markets are also problematic where customer feedback (money) is not rewarding quality increase (e.g. when teachers are rewarded when setting artificially good grades).
Edit: in my example the university could change from accepting all students with correct diploma to doing admission tests to resolve. I know nothing of the feasibility of this though.
Then people will choose their high school depending on whether they need that extra preparation, and those schools will have more students or be able to charge more.