And Google really should implement a "proper" (encrypted) backup solution for Google Authenticator. Relying on users to safely store the individual "secrets" themselves is messy and prone to error.
I agree with the suggestion to introduce encrypted backups, but not with the second part of your statement. At least we Bitcoiners should be well accustomed with storing weird strings (private keys) or a bunch of word combinations (the seed). I have a written copy of each of my 2FA codes that I use for exchanges and other services. It came in handy a few years ago when my old phone suddenly died.