Authy solves this by putting all the TOTP keys behind a master password and then backing it up online, so you can get up and running on a different device quick

Authy solves this by putting all the TOTP keys behind a master password and then backing it up online, so you can get up and running on a different device quickly. It's the same trade-off as a password manager, where your eggs are all in one basket but hopefully it's a secure basket.