“The universities have no motive to keep costs low when they know the Federal Loans will subsidize their economic malfeasance.”
That is the heart of the problem. In the triangle that is a student, Big Education, and finance (FedGov, banks, etc) only BigEd has no market pressure to control costs. BigEd will not let a student start classes until all charges are paid up front, BigEd does not care where the money comes from, and BigEd has no vested interest in the product they turn out (educated student).
One possibility is to force BigEd to finance some significant percentage of the tuition and fees they charge, say 75%. If they are on the hook for a substantial chunk of the loan, they will be more interested in turning out a student that can earn enough to pay it back.
If the college co-signer the loan,they would be much less interested in admitting unqualified students, or offering worthless courses.