Cool idea for a campaign!
Can I ask what stops the "professors" from solving all the real problems, leaving the PC's to do only the menial work? What's stopping this from turning into basically what people complain about when they complain about Elminster and Drizz't and Mystara in the Forgotten Realms: the PC's are just shoe-shiners?
Sure. It's an ongoing issue.
For one, it's not children as PCs, this is a University. So they're adults, just young. Danger is an accepted part of being a student, and though quests are intended to be non-lethal, lethality is a possibility of life at the University (though they try to resurrect anyone killed).
Second, in our game war was coming, and the professors were mostly aiding with that and giving the normal difficult tasks to the students.
Third, the professors had been infiltrated by the enemy, and so had the school grounds. So there was a lot of manipulation going on, and students were sometimes endangered in ways that the professors did not know about, with surprise challenges.
We did have a MASSIVE battle against undead at one point, and all the professors joined in. The sheer quantity of undead made it so the players simply contributed to the larger battle, and they had fun seeing their higher-level professors take out lots of undead while they did their part. Also, since the party caused the undead to rise in the first place, they had to defend themselves for many rounds before help from professors arrived.
Why don't the grown-ups fix their own problems? And how do the PC's rise above their educators to become heroes that those educators then admire? How does our druid trainee character become a hero that the 20th-level archdruid Gardner admires?
In our prior campaign, in general the adults had even worse problems to focus on, and also the PCs kept getting caught up in secret plots that the larger group of professors were often unaware of until it was already resolved. Often these were plots that caught them up because the foes were less concerned about petty students and so more willing to expose themselves in front of the students.