That sounds like it's a hard requirement for checking your bank balance/etc over the internet. Can't you just not do that and phone them up or go in person or read the monthly sent paper balances? Or just keep track yourself... A bank without a physical location is something I'd steer well clear of.

I barely use my bank's website and could easily not use it at all and still have all the functionality that a bank provides.

Paper balances and visiting your local branch are mostly a thing of the past. Calling them is an exercise in extreme patience. My bank all but discontinued actually visiting them except for certain specific things.

In the Netherlands (and beyond) online payments (shops, Steam, etc.) are made via the IDEAL platform run by the Dutch banks collectively. That is a good thing, because payments are secure and easy, and no one needs a credit card. But that does mean using your bank's web service to approve those payments.

Using the bank's offline OTP hardware (where you insert your debit card and enter a PIN and the code generated by the bank's website for an OTP) is possible, but using the app is significantly less effort than that. There is very little point in resisting it. It's not a healthy situation, but it is the reality.