My understanding is Mastodon requires the server to be complicit with the transfer (online and redirecting requests to the new destination). If your host server is offline or not willing to migrate your data, you can't move.
In the AT protocol, your identity isn't tied to a server. You don't need the older server's consent or support to have a new identity somewhere else.
> In the AT protocol, your identity isn't tied to a server.
It kinda is. Your identity is in the hands of whoever controls the PLC Directory. You can argue this is better than having your account and identity on the same place, but it still a third party that you depends on.