Student-Centered Education in the Middle Ages

In  both Marlowe and Goethe's works, Faust is a professor. Especially in Marlowe's work, we get a bit of a sense of what it was like to be a student in an early modern university. 

For a bit more background, I thought this was a really interesting article about medieval universities. It's a review of a seminal piece from 1930 called "Mission of the University " by the Spanish philosopher Jose Ortega y Gasset on universities. Ortega says we tend to think of the modern university as an odd, awkward hybrid between the 19th-century German research university and the British residential college. Ortega reminds us that universities also have a ver early Mediterranean tradition--and that this tradition was highly student centered. In fact, so student centered, that the model of a university was a group of students banding together and hiring their professors.

What do you think? Could you imagine a university where every year, the student government would decide who was going to be hired and what was going to be taught? Would it produce a good education?