I really don't like giving out my phone number to a small company with no apparent revenue model, no matter what they are saying they are going to do or not do with that number. Sorry for being cynical, but judging from all these services coming and going all over the place, any of the following is going to happen within a year: 1) authy gets bought by $COMPANY. With some likelihood it's not a company I want to have…
It's not hard to pluck SMS out of the air and sooner rather than later that's going to be a new attack.
Great one more thing to worry about.