When you first enable 2FA with Google you have to do SMS (at least that was the requirement last time I did it). However, once you've defined an alternative 2FA method (Google auth, u2f key, etc) then you can remove the SMS method completely.
Believe it or not banks are really bad at security. They are so bad at it that they don't even realize how bad at it they are. But the banks all copy from each other so "what the other guy is doing" is more or less their justification for what they do. Most of them have little to no idea why they do what they do for IT security, they just do what the Computer Security for Dummies book says to do (walk through the IT security department at any big bank and I bet you there is a dog eared copy of that tome on every desk)
Synchrony is one of the worst offenders, they won't even let you change your password without doing SMS verification, and their source of phone numbers is a Transunion skip trace database (which you can't change or remove any information from), so getting past Synchrony can be as easy as filling out a contest form at a mall, waiting for the phone number to appear with Transunion, then choosing that phone number to do SMS verification. It might take a couple months but payoff can be huge.
My hero at the moment is Capital One, they allow you to do e-mail authentication instead of SMS, and their iOS app also doubles as an additional factor (one requiring you to enter your password or use touch ID to use).
I was also extremely happy to find that the brokerage Robinhood offers Google Auth as a second factor. E*Trade also offers 2FA but a proprietary token w/ lcd display (which they happily charge you for).
My trick has been to give banks a false phone number that rings busy forever. That does effectively keep me from using banks that require SMS authentication, but there are more then enough that either offer other methods or drop their SMS requirement if you list your mobile number as your home number (indicating that its a wired phone and can't receive SMS). That doesn't keep my Synchrony accounts secure but there are enough protections around credit cards that my liability would be $50 at worst, with Synchrony having to eat the remainder of the loss.