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.
You know, I regularly lose or forget my baseball caps (at least once per Summer, and usually I go through 2 or 3). I wish there was a nationally-mandated register of headwear, with obligatory chipping at the points of sale. Not even entirely joking.
On a more serious note, it's interesting to note that some property never gets any ownership marks on it, some gets it customarily but only out of convenience, there is no legal obligation to do so, and for some property it is legally-mandated by the state but owners largely find it cumbersome.