Sure, but this still requires a certain level of "awareness" for this technology.
It's sort of the same problem PGP suffered from. It's technically great, but cumbersome for non-technical people to use (particularly in a safe way), so people will avoid it.
2FA needs to be simple and easy to achieve mass adoption.
Making people install special apps for just one service, or find out one day they're permanently locked out of their facebook account (or far worse) is simply going to hurt adoption.
If your grandmother can't make it work on her own, then it's not good enough. I'm not advocating SMS is the best option for 2FA, I'm just pointing out the alternatives are currently not up to snuff.