What does post office have to do with identity verification?

In the USA they already take passport photos. Being able to receive mail addressed to a name is the closest thing to a national ID the USA has. They're already depended on for identity verification quite a lot.

Some post offices in the US also function as a so called notary public. Basically, they can verify your identity and attest that it's you who sent/did something.

This is used quite often for important things that don't have offices themselves.