Tuna-Fish said that instead of backing up the keys from your devices, you should create a specific backup key that is only ever used in case you lose access to all your devices.

This is indeed best practice because it allows you to alert based on key: if you receive a login on a machine with your backup key, but you haven't lost your devices, then you know your backup was compromised. If you take backups of your regular key then it would be much more difficult to notice a problem.