This. Recently I had to send my phone away for repairs, and as instructed, they told me to reset the phone to factory defaults before mailing them the device.

This. Recently I had to send my phone away for repairs, and as instructed, they told me to reset the phone to factory defaults before mailing them the device. I forgot about Google Authenticator during this process so ended up having to reset everything/go through recovery procedures across all my accounts. With SMS it almost seems stateless, the only thing you need is access to a signal. That's the biggest advantage in my opinion, but given the risks I'd be open to ideas that are not just "download an app onto your phone"