Is Google Authenticator tied to your smartphone, to your account, or a combination of both? Can you transfer it to another smartphone? Is it being backupped automatically?
We're amongst a very technologically educated part of the population here, and honestly, I'm not sure about the scope of Google Authenticator. Quite sure that many aren't.
If you can extract the private key, you can transfer it to another phone or device.
On Android, AndOTP is open source (available on F-Droid) and allows encrypted backups. As for Google Authenticator, I don't think you can create backups.
With Authy, a Google Authenticator, on iOS the codes are backed up in iCloud and protected with a pass code. I’m not sure whether the pass code is used to actually encrypt things or just as a soft lock.
We're amongst a very technologically educated part of the population here, and honestly, I'm not sure about the scope of Google Authenticator. Quite sure that many aren't.