It seems to me, someone who has not looked into this much as if for several hundred years from around 1000 to until maybe the 1700's there were very few universities in Europe, really just a handful, and they had small class sizes as well. I know this is very hard to answer objectively, but did a disproportionate amount of new human knowledge come from these early schools, or were they predominantly social places for rich youth to enjoy some drinks and have a good time.
There were at least 53 universities founded in Europe before 1400. As far as my knowledge stretches one of the earliest consequences was an interest in formal training for clergy. Roughly half of English bishops by the mid 1400's were graduates. Beyond this, a desire to provide able administrators for the state led to the kingdom of Naples first university in 1224. Similar motivations were at least partly behind the founding of Oxford's first college.
(Roberts, J. 1996)