If you turn that card in at the hotel, you're giving them something from which that credit card information can be pulled off.
I just found that out myself. Now I destroy that plastic card. I take it with me, and when I get it home I cut it up.
I have a shredder at home, and I shred everything with my credit card information on it. A lot of personal information is pulled out of the garbage. If you put it out in the garbage, then it's pretty much open season.
You're quite right. There's a tremendous amount in terms of simply preventing it from happening that individuals can do to protect themselves and that business can do to help them protect themselves.