I'm sure they're done electronically in some places: Your passport details are appended to the shared Google Spreadsheet...
I'm only half joking: I used to work in payments, hotels didn't care about PCI. Full card numbers stored everywhere.
I know, and that's really the thing: nobody cares, not the government and certainly not the hotels.
I know, and that's really the thing: nobody cares, not the government and certainly not the hotels.