Question, when you move to a new place in Spain, do you need to register residency with the police?

I don’t know if Spain does that or not, but I think Italy does some version.

The United States doesn’t have that, and doesn’t have a national id card. Although most people effectively register themselves to get a driver license, that is only required if you drive. So voter registration nominally provides some way for the government to get the information on residency, which is important for figuring out which local elections you need to vote in.

Now recently, in the last couple of decades, some states started requiring photo id verification to vote. This defeats the purpose of having a separate voter registration system, because you still have to go to the driver registration system to get either a driver license, or a non-driving photo ID. Nevertheless, the separate voter registration system has hung around in every single one of these states, because the real goal is to prevent people from voting.