I agree, there are a lot of things that I prefer other people don't have access to more than I need to regain access to after losing it.
I don't care a lot about my old emails, but I care if someone else has access to my old emails.
I've never thought about this, but now that you mention it, I think is a great idea.
A service I'm building has this option. Puts protection against SIM/email jacking or social engineering into the hands of the customer if they feel capable.