If you start pushing insecure technologies like this, people will just get really comfortable with them and eventually get taken advantage of.
A secured data connection is much better than SMS and easy to implement. But this is still a 'something you send' factor, which can be intercepted. A physical token or 'something you have' is more secure, and can also be easily implemented with a YubiKey, a paypal/ebay authentication card, etc.
If you think your data is so valuable someone might install a keylogger to get it, you might as well secure it as well as you reasonably can.
Yes, SMS can be broken. I'm sure Google Authenticator is vulnerable to certain attacks, too. Using them is better than throwing your hands up in the air and saying "it's not perfect, we'd better not implement it because then people will act as if they have perfect security!" Because people are already acting like they have perfect security.
Yeah, SMS isn't perfect, and yeah, it's better than nothing. But you know what else is better than nothing? Properly implemented TLS from an app or website on the phone. Of course that has holes too, but it's encrypted and (hopefully) authenticated unlike SMS. And it's available in every phone that can do SMS (unless you don't pay for data).
You can do whatever you want. But if you give people a crappy option and a good option, and the crappy option is slightly easier, they'll use the crappy option. But if they want the extra security they'll use the extra click it takes to make the good option work. Most people will just reason that nobody will ever use a keylogger on them and keep using keys with passwords.