The title of your post makes it sounds like a temporary space was setup as the brig, rather than what your post body says which is that Archer never held a person for a long time in the brig.
A brig on a ship is generally not for long term use, it's for stashing people until they can be delivered to a proper prison. So it makes sense that Archer mostly uses it as a place to stow people who can't be let loose on the ship for a while.
Then he comes to them and asks for information or whatever, and they are turned over to the custody of their people or whatever is called for by the mission. Remember, there aren't extra crew quarters to be "confined to" like there are in something much larger like a Galaxy class ship, so the Brig it is, since it's designed as secure facility.
So the idea that they are always let out at the end of conversation is mostly Hollywood shorthand, the person has been put in the brig for a while, and then we don't see them on camera since they aren't important to narrative for the time being, the next time we see them is when Archer comes to the brig to talk to them.