You already can do that. Just buy a domain name, like mySSN.us. You are free to point it at any email provider of your choosing.
Also it's kind of technical. Perfect for a nerd like me, but e.g. for my mum? Nope!
It is a bit technical, but that can be solved without involving the government. You just need the registrar and email providers to talk to each other with OAuth plus some DNS delegation protocol.