Seems to be the same thing with the BlizzAuthenticator. Good idea, but I wouldn't use it. You gotta consider what happens if you loose your phone. You can't do any emergency calls and don't even have access to your saved phone numbers anymore. You're also locked out of your Gmail Account for god knows how long. I like my phone, but a little bit decentralizing can never be wrong :)
I have a relative with a fire proof gun safe in another state. This is a good place for crypto keys, master passwords, etc. For the cost of overnight Fed Ex, I can recover from a disaster.