Do you live in one of the European countries that has a registry of all citizens? At some point, the government needs to have some notion of who you are. The US has no central registry, so it gets pushed out to the periphery like this.
The problem is that they aren't interconnected in any meaningful way by design so the bulk of the work gets pushed onto states. Real ID forced a lot of the states to get their act together but it's still a bit of a goat rodeo in places.
There's also birth certificates, which are state-based databases, AFAIK, so there is that route too, and that process is more along the lines of how we're a federation.
(& for voter registration, probably the most common method, at least IME, is to bootstrap that from your state license/ID; since those are generally REAL IDs now, most individuals would provide birth cert and SSN, since that is the most broadly fulfillable requirement of REAL ID.)