I use Google's two-factor authentication, because I know that access to my email account is the skeleton key to all my other accounts.

And... it's pretty annoying - I'm frequently swapping computers and other devices, and use a lot of native apps that need access to my google accounts, but I know it's the least I need to do to protect my email, since it's the only thing between me and ne'er do wells who might want to reset my Netflix password and stream bad movies that could muck up my recommendations.

The primary way to get the login code you need (in addition to your passoword) for Google's two factor auth is through the Google Authenticator app that you can install on your phone.

But, if you don't have it installed, or it's not set up, or something else goes wrong, they'll send you the code via SMS, which is presented as more of a backup method. Which brings me to my question. Assuming I'm comfortable with the security of my SMS communication:

Isn't SMS a better way to get the codes, at least from a convenience perspective?

If I disable authenticator (triggering SMS codes), whenever I need a code, it's instantly pushed to my phone, with no actions from me, and appears on any screen I'm on. I'm done.

With Authenticator running, I have to unlock my phone, open authenticator, pick the right code (I have two Google accounts), hope the code's not about to expire (the text sends one that's "fresh"), etc.

I completely understand that SMS is slightly less protected: Someone who has my phone (and presumably my password), but can't unlock the phone can see the SMS notifications, but couldn't open Authenticator. But that's a long shot. There's also the fact that services like iMessage push SMS to other devices, like Macs, iPads, etc. But again, assuming that I'm good with my control of access to my SMS:

Is there any reason to use Google's App vs. just getting texts?