Here are the reasons to avoid Google Authenticator
If you set up google-authenticator in your phone and you accidentally lose it, you won’t be able to access your google authenticator account ever.
Even though you might have thought that you kinked the authenticator app with your Google account/Gmail, you won’t be able to get your previous set-up codes.
You might think that simply logging into your new phone and setting up the authenticator app with your previous email/google account will restore your authentication codes.
This is however false since you won’t get access to your previous codes and will be forever locked out of the account you wanted to log into with the only option being contacting support to recover access.
Uninstalling and reinstalling the app also leads to the same problem.
The app doesn’t have native passcode or biometric lock feature. This means that you’ll have to use third-party apps if you want to lock your app from prying eyes
I would personally recommend using Authy by Twilio. It allows you to create an account, backup your codes, access the codes from multiple devices, multiple operating systems and offline access.