It would ease debt servicing for existing student debt holders, creating consumer excess (just as lowering rates for mortgages creates a wave of refis, which puts more disposable income in America's consumer pockets).
The key would be for the Fed to restrict its activities to existing student debt, to prevent pushing down rates on new originations.
Student loan rates are set by Congress, and student loan consolidation does not generate a bonus at closing. As a result, there's no direct consumer surpluses to be gained by having a separate owner of student debt. At best, the Fed buying student loans would benefit Sallie Mae/Navient, because the Fed's purchase price would have to be higher than their preferred holding price.
The key would be for the Fed to restrict its activities to existing student debt, to prevent pushing down rates on new originations.