This is excellent advice. You might not be able to write on, for example, a passport taking a photo of, but can certainly put a postit note-type sticker on it.

that is a good idea but most of the time I need to hand over my actual ID, and not just a scan of it

I'm usually an uncooperative bastard at times like this. I ask them what their purpose is in retaining a copy of my identity document, and I ask for their privacy policy. When I'm travelling for work and a hotel asks I simply say no, and remind them I can lodge a complaint with our corporate travel provider that will have them delisted for future business; usually they come to their senses. For overseas travel (where they often have to fax your passport to the police) I ask for the photocopy back when I check out; since these documents are lost/misfiled regularly the desk clerk usually complies. Always try for point-in-time ID verification rather than retention.

I used to be uncooperative too but in the end, I usually have to still give it (or go somewhere else)

Where do they ask you for a copy of your ID? I've never had that happen to me at a hotel.

It's because of credit card fraud usually, they want it to prove to credit providers that the actual card holder was present, and if not, exactly who. And I've been asked in countries across the first world, though I haven't been keeping specific note of when.

Yeah, like most doctors offices will take my license with my insurance card, and they scan them into their own systems to associate with my record. No opportunity to insert my own add on content. Just hope whatever SaaS based patient management system they have is iron-clad secure. (But it isn't)

I guess you could stick a very small sticker on it