To elaborate: note that if a property asks for a plate #, it's probably written on the registration cards which are typically filed in a box at the front desk. Especially at a limited service property, it's not going to be that difficult to get your hands on that box for long enough to e.g. snap a picture of a reg card of interest. The reg card will also have a confirmation # and a guest address, but if you're in Honors and have a PO Box in your profile that's probably sufficient to shield that. You can also take steps to shield your registration info (LLC etc.), but there are plate databases maintained for repo men.
These databases are filled in by roving cameras taking pictures of every car they see and recognizing the plates. Chances are that your car has been picked up many times at all hours by these, and it's not that expensive to buy a report of places with times that your car's been spotted: from that data it's easy to deduce where you live/work given your plate.
Granted, in the confirmation number scheme, an attacker could go from knowing you're in room 316 to getting a confirmation number to finding your car and plate in the parking lot and finding out where you live and hacking you to pieces in your sleep, but the hotel asking you for your plate makes that a little easier.
I don't think this is worth being paranoid about, for the record. "Plenty of people will kill you for some fanatical cause" and all that.