Apple Arcade does the same thing on the TV when switching between Apple IDs from countries where Arcade is available and countries where it's not.
So my girlfriend's ID is from Hongkong where it is not available, and mine is German, where it is available. No matter where I put the Arcade app, even into a folder – when I switch to my girlfriend's account it disappears and when I switch back, Arcade reappears in the middle of the dock, pushing the app utmost to the right of the dock out of the dock. Super annoying since I don't want to have Arcade at all but I can't even delete it.