No, because most banking apps call upon the Google Play Integrity API, which GrapheneOS doesn't (or can't?) use. There's a decent list kicking around of which ones work (Monzo, for instance).

https://privsec.dev/posts/android/banking-applications-compa...

> this also sort of defeats the purpose

Not really. On GrapheneOS, the Play Services/Play Store run as sandboxed apps, i.e. they are not system apps like on Android. They just run like a normal, unprivileged app. That's a lot better than on Android.

> I'd rather break free from Google and Apple, not just (stock) Android and iOS

If you want to break free, you don't have to install the Play Services / Play Store on GrapheneOS, just like you don't have to install microG on LineageOS. There is a misconception that microG is better than sandboxed Play, but I disagree. With microG, your apps still connect to the Google servers, so you're not "breaking free".