I know of a trophy you only get if you draft 9 copies of a specific room in a single run, but I don’t think trophies are necessary to progress with other parts of the game.
About missing rooms: get the drafting studio, it allows you to add 8 additional rooms to your collection one by one. I don’t know anymore if the one you’re missing is among them, but I think so.
You might be right about the machinarium, that seems to be unusually hard to get for a sanctum key. I haven’t thought about it yet.
9 of one room is easier than that, it’s a very specific room.