One of my banks (Starling) is app only.
Some F2A I've used only operate using notifications, which while is a bad design, requires notifications to work
They started to require to type my own account password into websites to be able to pay via credit card! Incredible but true. As this was of course completely unacceptable I resisted for as long as I could. But at some point I had to use my credit card on a website with no other option (it was for a collective present, I couldn't select another website; I could not participate but that would have been incredibly rude and unkind).
It's not too horrible though. The app is much less bad than I expected.