"There's a barrier around the place keeping the ghosts in, so if we just get rid of the barrier, maybe there won't be as many ghosts"
How exactly is the one who suggested this smart enough to be attending academy? If the barrier stops working, it's not like the ghosts will disappear. They'd be turning one problem in one place into lots of problems in lots of places.
And another thing, has the academy fallen on really hard times or something? Can they really not just hire a priest to take care of this little ghost problem so they can go back to using an entire campus building? Not dispatching priests as teachers because one student beat one up twenty years ago isn't the same as refusing to provide a service that it seems pretty much only they can do.