It's important to the USPS because the reason they want to know a person's identity is for the purpose of physically delivering mail to the correct address for that person.
> what about states that don't reissue IDs when someone moves
Do these exist? I'm not aware of any state that doesn't require you to update your address when you move.
> what about states that don't reissue IDs when someone moves
Do these exist? I'm not aware of any state that doesn't require you to update your address when you move.