Where I live I already have to provide my babysitter a signed letter where I certify that she comes to work here. She's from a different township (comune) and the police could fine her if caught without that document.

It's not going to stop 100% of people from moving around, but even it this reduces the spread by a few % it's already a big improvement; even reducing the daily rate from 21% to 20% can have a 20x effect on total cases over a year.