I'll start by ignoring the technical and social difficulties (domain name changing... causing troubles both for lookups/computers as well as humans who remember the old address...)...
What you mention first, @bjoern
, is not account migration. "Without having to start from scratch" and "without losing your connections" is only the transferral of subscriptions. We could discuss bi-directional transferrals (but why would you be able to force a remote party to subscribe to a new, possibly untrusted, server?!).
The "right to move" is still there. Restoration of backed up data is however incredibly hard to do without breaking the laws of physics.