I find it very annoying that they just stay in the place of kings, right in the main hall, after ulfric has been brought to justice. They should at the very least be put in a jail cell in the bloodworks. Anyway, is it safe to just "disable" them, their exiled stewards and housecarls?

I dont think so. I have a feeling there gonna be needed or used if they do the moot in a dlc. I see them causing a disturbance or at the very least being used in some way.

You can do that. You'll enable them anew if needed in the future, using the commands:

prid id_of_the_jarl [enter]
enable [enter]