My bank doesn't yet require the mobile app (quite), but all interactions are significantly more annoying without the app. My 2FA options all require a phone, either for the insecure method of texting me the code, or else an app-only option (they don't allow generic 2FA apps, but instead require a specific app, that almost definitely won't exist for a linux phone). Even verifying my identity on the phone is better with the app (the app generates a code that they just accept, it can be done without but it's slower and more inconvenient).

So no, my everyday interactions don't require the phone app. But any interaction that is novel enough to require direct communication with the bank has been rendered annoying without the phone app.

I'm someone for whom I'd probably be willing to deal with all these inconveniences to make my statement about ownership over my hardware and software, but I doubt that very many average consumers would.