> but the post office already issues US Passports.
The State Department issues US Passports, the Post Office merely accepts your applications on their behalf.
> I'm not sure what you mean by "verifying mailing addresses" because the USPS does provide a way to do verify the correctness and deliverability of an address [1].
It's only vaguely tied to identity. I have my physical address, but because I live in an RV park and move often, I don't actually receive mail there. In about half of the locations I've stayed, you _can't_ receive mail there.
I use a private mailbox along with a mail forwarding service in order to receive postal mail.
> [1] https://en.wikipedia.org/wiki/Address_Management_System
Is used to solve the problem of sorting and routing mail, which is really what the Post Office spends most of their effort on. Every postal address in the US can be uniquely identified by an 11 digit code: your ZIP+4 and the last two digits of your house number, but it completely ignores multi-tenancy and has no provisions for linking to identity.