Then people would complain that disadvantaged students are being denied high education, because such students inevitably are going to have worse academic prospects than well off students, and therefore can't get student loans.
So you expect private lenders to be on the hook for delinquencies and put them in charge of assessing credit risk, but then at the same time kneecap them by not allowing them to see any information about the lenders aside from what degree they're studying? Seems like a shitty regime where the smart middle class students (not rich students, because they don't need student loans) bears the burden of subsidizing all the bad students.