Mobile phone authenticator apps are not that great anyway. They rely on the security of a phone that is connected to the net to keep the keys secure. If someone can get code running on the phone and exploit a privilege escalation vulnerability to get root, they can read the keys. A hardware token like a Yubikey or similar is probably more secure.

Another problem with the Google authenticator, at least for Google accounts, is that you have to add a phone number to your account to use it I think and, they then allow access by SMS, which is not so hard to circumvent.