You will recall me saying I was going to contemplate the purpose of the Day Gate further.
I have found a section where at the beginning of Apert someone presents a tree to the Mynster in memory of their father who liked to enter the day gate to attend lectures and use the library. My theory, and I don't think there is anything to contradict this, is that people can essentially come and go as they please from the Unarian Math. The Year Gate is essentially symbolic i.e. people 'signed up' for a year can interact with the people coming and going through the Day Gate. I assume that effectively anyone can attend lectures but only people signed up for a year can go to tutorials or their moral equivalent. I imagine that people who are following the Discipline have to wear the bolt. This is, I guess, a bit like where you see people wandering round Bangkok who have signed up to be monks for year and who wear yellow robes. Except of course that they are allowed out whereas Oncers can't go out through the Day Gate, or rather if they do they have broken the Discipline and are thrown back. People not staying have to leave at sunset by the Day Gate.
I think this makes more sense e.g. in the context of the hospital inside the Mynster which is clearly not just for avout.
Remember that Erasmus is an unreliable narrator and isn't particularly interested in how the Unarian Math works.