This assumes that a lender's primary interest is in having a loan repaid quickly. I don't think it's true - they are in it to make a profit, and exploiting the young adult with penalties and hidden fees or tricks helps expand that profit.
I think one good reason for government participation in the student loan market is that it helps reduce exploitation of the borrowers, who are mostly just-turned-18 adults so eager to attend a college they'll sign anything.
The idea that all education at any cost carries positive externalities is exactly what got us into the mess that is education today.
Edited to add: Also, my proposal isn't incompatible with neither financial aid nor grants to institutions. But like underpriced mortgages caused a housing bubble, underpriced student loans is causing an education bubble.
Time for me to find some investors and pull my own Kyle Bass :P
[0]: http://m.washingtonpost.com/business/economy/sallie-mae-to-s...
If you want to see what happens when a society mindlessly thinks "more kids in more college is better, damn everything else," look at society right now.
Those out to study degrees that don't offer great employment opportunities will be offered more expensive loans which will curb demand for such degrees which will depress the cost of the degrees. It will also make sure that fewer people will go to a party college and study an easy degree (or, at least, that those that do aren't subsidised by tax-payer underwritten credit).
Extra bonus: All those companies that clamour for STEM grads have a very simple avenue for putting their money where their mouths are: Simply go out and underwrite some cheap loans. (And no, indentured servitude is still illegal - companies underwriting student debt shouldn't be allowed to change the terms of the loan if the student comes to work for them).