I don't know which banks you are using but in my case I work with five Spanish banks and I can do everything from their websites, no app required. Yes, they try to push you to use their app, some tried to activate mobile 2fa for me when this psd2 thing became mandatory but I always told them their app doesn't work on my phone (which is true) and they offered me alternate methods like sms.

In my country we have a large religious population who eschew the smartphone. This means that no government, banking, or other services require a smartphone.