These are exactly the issues I'm dealing with in re-implementing two-factor auth in my own app. On the one hand you can easily roll your own SMS based TFA with the option to use Google Authenticator with a negligible amount of work. Google's app is pretty reliable and most people trust Google (rightly or wrongly is beside the point here).

But then what if Google pulls the rug out from under apps that rely on it and what if knowledgeable users like you don't like the idea of a third party having access to their second factor?

I'm starting to think that unless you're willing to build your own authenticator apps for multiple mobile OSes SMS-only is the best way to go.