More bluntly, what is it that you think your current registrar is lacking?
I read a few comments on Gandi and support of GPG keys. I'm guessing this is what you're referring to: https://wiki.gandi.net/en/gandi/documents
Customer support should not be able to see anything about these accounts except for a reset button. I do expect to be charge a fee for a reset if I need to use it. This would need to be rate limited to prevent people from dosing an account through it.
If you want them to go thru the trouble of mailing something, at least require it to be a letter. Inside an opaque envelope.
A postcard is the exact opposite of something you want to use to send sensitive information.
Let users chose if their account can be recovered through a password reset form, let users leave 'secret memos' for support which can't be viewed on the site later, let the users decide if their accounts can be altered in any way by support staff, etc, etc.