As someone who plays a character who is almost always the idiot who left the gate open, there is a limit to how many times a character can do that before it starts really wearing them down and make them harder to play, so I very much understand that concern.

Might be good to have a heads up which arcana would be in which jaunt on voting so that people can request walkabouts to just avoid the situation entirely, or even have a secondary "So knowing which arcana are involved, who needs a walkabout now?" option. (Since that is sort of the whole point of walkabouts, isn't it? Avoiding putting your character in a messy situation...)