As I understand it, the problem with this approach is that even the pre-2010 system put the risk of default more or less completely on the Feds, as it is now. If you leave that risk there, then market players have no incentive to set rates themselves: It's up to the Feds to decide which loans at which rates they're willing to backstop or acquire. Not really a "market".

But if you move the risk of default onto the "market" via private lenders, then, the theory goes, the rates a student can expect will be swamped by other factors than the value of their prospective education, notably whether they have a sufficiently credit-worthy parent to cosign.

Maybe the best bet is to have market rates that are "cushioned" by the Feds in a need-based scheme.

Do they? If government loan programs treat all degrees interchangeably, why do you have differential pricing for STEM degrees and Liberal arts, with the latter being cheaper and STEM, law and medicine degrees being the most expensive.

They are more expensive because the programs cost more to run. The professors have more job prospects outside of academia, so that drives up their wages. They also need more expensive resources (labs, legal libraries, etc.).