>OK, so your social security number is your "digital address", and the post office has a database of everyone's current address.'

No, not really, Yu-ID is not the same as the My-ID (akin to social security number). So you wont have to reveal your social security to your taxi driver etc. if that was what you worried about.

>If you move you still need to notify them, although perhaps in Japan big brother already knows you've moved.

Yes you would have to change the physical address for your Yu-ID, but you don't need to tell all your acquaintances to update their greeting-card address list ( they can still send to the same Yu-ID)

Another case might be that you are temporarily living at a 'summer-residence' , or that work takes you to a new locations for months at the time.