> Isn’t this a problem with _any_ type of 2FA?
Not quite because if you lose your YubiKey - you just lost your YubiKey, you still have the ability to call the bank (and my bank knows my number, so they greet me by the name) and at least do something, in the situation I've got in the previous comment I could lift the lock out with the code word, only if I could recall it then.
But the phone is not only your 2FA item, it is also your "virtual identity" now for too many services, banks included. And with the tendency of banks to shoehorn you to their phone apps this starts to get ridiculous, if you lose your phone you are now:
lost your banking app (2FA with push)
lost the ability to 2FA with SMS as a backup
lost the ability to install the app on the new phone (oh hi $username, it is really you despite you just gave your $username@gmail.com and password? We sent you an SMS to confirm it is really you, FOR YOUR SAFETY)
lost the ability to login to your bank account on someone's else phone (same shit with SMS to your phone number)
Bonus points: if you lost your ID or doesn't have it on you - you can't restore the SIM with your number. Or even buy a new one in many cases.
> But, if the user has chosen to use 2FA (or has not opted out), what’s wrong with SMS?
Pfft. I was forcefully shoehorned to mandatory SMS 2FA by my bank. I've opted out of this some years ago and it did work... till I was 600km from my home, I needed to buy the train tickets, I tried to logon to the bank webapp to move the required amount to the primary account only to discover what they enabled 2FA without asking. And the phone where my SIM (known by the bank)[0] was installed was literally on it's last 10% of charge in the airplane mode. It could literally shutdown just from the act of disabling the airplane mode so I could receive the SMS.
So if the problem is not with SMS 2FA. The problem is what nowadays "SMS 2FA", at least for the banking apps[1], is way, way more than just SMS alone.
[0] I'm not sure if they monitor IMEI of the device, but I wouldn't be surprised, considering they receive the notification of the changed IMSI.
[1] Not sure how these practices are widespread world wide.