according to the story, the post office did better than any phone provider would. he moved to a new location, maybe years later, and a piece of mail still followed him to his new address. i'm sure the registry gets notified of forwarding address changes for people on their lists, so they could in theory keep up with you even if you moved a bunch of times (as long as you forwarded from at least your last address).
if you get a new phone number, your old one probably won't forward to you, and once someone else has that new number, you will never get forwarded calls. at least with a mailing address, new people can occupy that same old address but any mail to it will still forward based on your name.