But there is a important point here too - these loans are issued with too low of an interest rate BECAUSE they are guaranteed by the government.
Drop that guarantee and the interest rate is going to float to more of a credit card level, which will make them prohibitive for funding tuition, which will put an extreme downward pressure on tuition rates.
Getting the DoE into the student loan market was intentional and is seen as the first step to reworking the entire system. Navient et al are keen to keep the gravy train rolling.
Minor nit: The gov't doesn't give the loans, they underwrite & insure the loans.