Turns out the local policemen asked verbally to make photocopies, just in case... The hotel is more afraid of the local police than of it's clients, so they just do it.
Since I was the only client who ever asked about it, and gaslighting me wasn't going to work ("everybody does it! what do you have to hide?"), they just gave me the copy to destroy.
Other places copy IDs because they're lazy and don't want to compile the required form on the spot. Not to mention ID photocopies floating around the reception desk in plain sight...