You wouldn't need a $10,000 loan for college if the money wasn't guaranteed and competition was allowed.
All the govt does by subsidizing loans is do what it did to the housing industry (and any industry it tries to control) it super over inflates prices, artificially creates a false demand, and drives institutions (in this case people) into debt they can't recover from.
When the govt guarantees loans to anyone, there is no competition. Colleges can set whatever price they want because govt will pay it.
That's what drove house prices up, when EVERYONE can get a loan, house prices soared because there was an incredible amount of demand.