MFA is a requirement of the revised Payment Services Directive (PSD2) in the EU and many banks use their apps for authorising online card payments. Its also common to use apps as 2FA for logging in to online banking or making bank transfers.

There can be alternatives in some cases (some banks offer code generating card readers, for example) but for personal accounts in particular, it would probably be difficult to operate without banking apps.

galvin@ is right. I +1'd that. Regarding banks ... try HSBC. (I know, "I can always use another bank". Thanks. I happen to be Premier only at HSBC ...)

This must vary a lot by location.

In Singapore, the largest local bank, and three large overseas banks (Citibank, HSBC and Standard Chartered) all require my to be near my phone to login. However, I haven't tried just saying I don't have a phone from the beginning. I know they used to have physical security tokens, perhaps they still would have provided one if I had insisted.

In New Zealand, I've only come across one bank that requires you to provide authentication from your phone (Rabobank), and in Australia I have less experience, but it's not universal either.

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.