In the case of my bank, I'd expect to walk into my local branch with my driver's license, passport, birth certificate, and any other official ID I have, and convince them that I am the same tzs who owns the account and have them set me up with new account keys.
What I wish is that there was some way to tie my other accounts, directly or indirectly, to my bank. My bank account is the most recoverable account I have, because they can handle me showing up in person with ID.
Other accounts just know me by my knowing the account password and/or being able to receive emails at the email address associated with the account. If either of those is compromised I can lose the account with no way to recover.
If there were some way I could have my bank verify my identity to my email provider, and tell my email provider that if account recovery is ever needed on my email account to re-verify with my bank that it is really me requesting the account recovery it would be much safer.
(If you are using an email address at a domain you own, then replace email provider with domain registrar).
Then no matter how badly I'm compromised (as long as it is not by someone with sufficient resources and interest to be able to get past an in-person identity check at my bank), I've always got a path to recovery.
Worst case, first recover the bank account in person. Then recover the email account using the bank account. Then recover compromised accounts that are using the email account for verification.