“Hello thanks for calling. I understand you want to reset your password. To verify it’s really you may I have your cryptographically impregnable super token? Oh it’s lost, I see, how about can you verify your billing zip? Splendid you’re all reset.”
Suppose you lose all your physical keys: I don't think you can social engineer hack Coinbase (pretty sure most companies won't allow people to just give away your password/send a reset email to some other email).
Or suppose you get them to send me an email to reset my password. But my email also has FIDO u2f! And I know as a fact you can't social hack my email provider.
The Google Authenticator app on iOS doesn’t backup its keys so it’s pretty common for people to lose access to that kind of keys.
Which keys is it supposed to backup?
Everything else you said is sadly true.
Under the hood Google Authenticator uses keys to generate the codes you see on screen and these keys are not backed up.
It’s a difficult decision of course. If you back them up in iCloud Apple and people who hack your Apple account have access. If you don’t the keys are lost if the device breaks or is lost and you need a workaround.
Edit: oh you wanted to restore on the same device. Well that might work but it doesn’t help when migrating or if your phone is not available.