Allow Proton Authenticator to Sync codes to Proton cloud.

Google allows me to sync my list of Authenticator codes to my account in the cloud.
If I lose my mobile phone, and can access my Google account via a recovery method, I can then access all of my data, including my Authenticator codes list, and re-download it onto the Google Authenticator app on a new phone, and I am back up and running.

Without this cloud sync feature, I am wary of adopting Proton Authenticator since losing my phone amounts to losing access to all services - and potentially finances/crypto.

Is this a sensible feature request?
Is there a privacy/security reasoning why this shouldn't be implemented?
Am I missing something fundamental here?

Thanks