Don't know about banks in Europe but in USA, I can log into Bank Of America and JP Morgan Chase without any phone authentication.
If I reformat my harddrive or buy a new computer and the bank doesn't recognize the web browser because no previous cookie has been found, the website will generate a one-time code and send it to my email address. I then enter that security code and the web browser is "recognized" without further issue. The smartphone was not needed in any step.
EDIT ADD: I did open my bank accounts before 2007 and thus before the smartphone era. Because of that, there may be a possibility that my logins are "grandfathered in" to not require any smartphone app authentication. It's possible that opening new accounts today with BofA/Chase require smartphones but somebody else would have to confirm/deny that.