In my experience, it's not really about the individual pieces of information, it's more about being able to build a more complete profile of someone. Most verification is built on the number of factors to build a trust score and having something with a picture, address, and additional ID number would give them another factor. That might be enough to put them over whatever threshold they need to open a bank account, credit card, loan, whatever.
What's the worst that could happen to you if something goes wrong during your hotel stay?
Because with your ID copied, that could happen to you if something goes wrong in your ID copier's stay.
Many lives ago I worked for an adult-webcam site. There we received a lot of webcam-model applications with real(-ish) passport, with the facepic photoshopped to the applicants real pic (Very frequently because the applicant her/himself was underage) Every day 10s, sometimes 100s of applications were rejected due to such shenanigans.