This. I relocated a couple of times recently, and am about to relocate again. I too contemplated about a similar service. Personally I'm not too worried about the privacy aspect as much as about the pain of notifying every single service provider when I change my address.

It does open up some interesting use cases. E.g., when I go on vacation then hold off delivery, if it's from Amazon then deliver it to such and such a post box etc. I'm not sure about the market size though.