Remove the guarantees, and banks will actually have to do their due diligence on credit risk. No need for clunky regulation, when this is what the credit market is for.
2. More people would "get to" go to college, because 1.
3. Those who do get loans, would get loans proportional to the value the education will generate.
4. Unprofitable majors will become cheaper to take.
Also, this isn't just about student loans, it's an even bigger problem for mortgages.
Making them dischargeable from the start would have stopped a lot of problems from forming, since borrowers could just default, thus lowering the average education fees due to downward pressure on loan amounts, and tightening lending requirements. Nationalising loans and only requiring repayment at high incomes would make them easier to deal with - the repayments just out of your tax, are only added at high tax brackets, and lower your borrowing capacity. Sitting in the middle of the two sides is the problem.
The market can't adjust itself because it's not broken; everyone buys houses because it lets them avoid future rent hikes, and basically everyone needs to buy/rent a house near their job if they don't want to go broke, so there's a huge captive market.
Remove the guarantees, and market will correct itself.