If you think photocopies kept in some folder accessible to anyone working in the hotel, with a promise to delete it at some point, is "secure" in any way, I don't know what to tell you.
When I toured apartments they would often take a photocopy of my ID. Okay, overkill. But realistically I have no idea where that photocopy is stored.
Probably in a OneDrive somewhere to this day.
Rather a paper data breach exposed to a few hotel employees than eletronic data exposed to the entire planet!