Yes, many countries in Europe. Germany, Austria, Italy, Switzerland, France, Spain, etc. When checking in to hotel, you have to fill in a form with your personal details, incl. passport number, car number plate, etc.
I think this approach is much too early. A few years ago the doctors were not able to deal with my sinusitis during 3 months. Back home the doctor gave me the right antibiotic, and the sinusitis was gone in 3 days.