phi maybe this is a social layer problem rather than a technical problem.
Your issue means a lot in a world where we have amateur hobbyists setting up social network servers and allowing the general public to join. Those hobbyists get overwhelmed or bored after a while, or they do a bad job and your server gets defederated.
In this case, it makes a lot of sense to move from one server to another. But this is not the only way we could organize the Fediverse.
Email isn't like that. You (probably?) don't use an email address from a server you found on a list on joinemail.org. You probably, instead, have an email address from your employer or university, and maybe a personal one from a well-known and reliable cloud service. If you're very clever, you may use your own domain for email, and share it with your household or family.
In those cases, you rarely change email addresses. We have some ad hoc ways to move from one to the other, but they aren't built into the SMTP or IMAP specs. And yet we have a lot of email going around, even after 50 years.
I think we should be putting our efforts into getting Fediverse services from organizations we have a lot of affinity with, like employers or universities or the city you live in or the post office.
Another option is using the extremely portable identity system we already have -- domain names. It should be a lot easier to bring your own domain name to a Fediverse server, and to move your data between servers by backing up and restoring and then repointing your domain name to the new server, like you do for blogs. This is really hard right now.
I think LOLA is doing a good job with online moves, but we should also be encouraging more server developers to support BYOD, and we should encourage Fediverse users to get a domain.