Ironically, that would enable tracking much more than the normal case, which is a hotel stores the scans on a hard drive on the closet that nobody every looks at unless they get a subpoena.
That's not what happens in Italy, at least - the documents are scanned and uploaded to a police portal in less than 24h. I expect that's roughly the same elsewhere. (I honestly did not know until today, I just knew the police would come every night to collect copies - good to see some modernization...)
