As long as one keeps the original string and or qr code safe (in a separate password database), TOTP can be put in multiple devices, is backed up & will not get locked out of accounts. But also, at the same time, none of the MFA setup flows on any website tells user to keep "this" string safe. Once that string is gone, there is no way to recover it.

I have a printed sheet with all those strings and their account names in my own memorized encoded form (like rot13). Plus my main phone, my backup phone, my tablet, all of them have same app & codes (all devices have fingerprint & pattern locks).