Teachers
In more general terms, what is the role of the head of each house? McGonagall shows up to intervene in Gryffindor’s internal discipline only in Harry’s third year.1 Harry finds Luna wandering the halls barefoot, posting flyers listing her stolen stuff, and Flitwick does nothing.2 I have a page dedicated to McGonagall, and it would be hard to write too much here that would not also go there, so these two examples will have to suffice for now. It seems that the school expects the prefects to run the school. I am unsure how typical of British boarding schools this is, Stalky of Stalky & Co. by Rudyard Kipling goes on an extended rant about the evils of married teachers, and how it puts too much responsibility on the prefects.3 Stalky & Co. is certainly idealised, no doubt in a lot of ways, but if you read carefully you can tell there is a lot of bullying, it is a rough life, but it is kept sufficiently in check that most of them come out of it … typically British (see the quote on bullying in the Students section). If Stalky thinks that it would be worse if the teachers he describes do less, well, then we have to assume that the few phrases we have hinting at the problems within Hogwarts are actually understating things.
Look at the roles that play out in Stalky versus Harry Potter. In Stalky we see prefects giving out discipline, including corporal punishment, but each house has a head that advocates for its students, steps in for discipline problems within the house beyond the scope or abilities of the prefects, and is generally present and visible not just as a teacher, but as a head of house. Indeed, in Stalky, the prefects are rarely mentioned, several of the school masters who head Houses are the most frequent disciplinarians (this might be because Stalky has the prefects totally intimidated). The Head is called in for exceptional problems, and if I recall, the punishment is made especially severe to discourage “bothering the Head.” Does any of this sound like Hogwarts? At Hogwarts every problem most likely not at all, otherwise by the prefects, and finally, by Dumbledore with Snape attending as advisor, no matter who is involved. Never mind McGonagall is Deputy Head, and therefore more logically the advisor at that point, we need a more Charles Dickens feel about it. Which is probably precisely the point.