I have several accounts in different banks (across two different countries) and never had problems with using SMS as a second factor for internet banking. Definitely not status quo, at least in Europe.
I'm in Europe and my bank (and most other banks in the country) only still allow existing TAN authenticators until they break or run out of battery, but only support 2FA with their app going forward.
Interesting that you mention Europe, because if I remember correctly, at least in Germany, all banks that I'm aware of dropped SMS support when PSD2 was introduced.