What city requires you to register your pet and get a license? I’ve never heard of that before. Sounds kind of crazy. I’m assuming this is very regional.
If I remember correctly, EU will make chip tracking for pets mandatory by 2030 to unify laws that are currently made by individual states. France had this mandatory for over a decade.
If you want to travel within EU with your pet, you'll need a certificate for that as well.
No idea about how it is is the US but that doesn't sound crazy to register pets as they are at risk of being lost, abandonned, lacking vaccination or vets visits.
Out of interest, why does it sound kind of crazy?
Here, pets have always had to be identifiable: historically with a collar, but microchips have been required for some years now as a more effective method.
(That applies nationally, not some city thing)