Medicare in the US has negotiated rates they will pay for medical services. The "retail" price is very often extremely high but knocked down to what the government agrees to pay for Medicare patients. A similar system for college loans would allow the government to still offer loans but with caps on how much colleges could charge for tuition to students with government loans. The problem is uncapped tuition and loan terms that allow lenders to offer tremendously large sums of money to students in a low risk way because the students can't declare bankruptcy or discharge the loans in any easy way.

Many of the largest schools in the US are government institutions. There's no need to negotiate prices, state legislatures can just set the price.

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