/e/ is being built to avoid being dependent on Google, primarily. Banking Apps mostly depend on Google (especially on Google’s SafetyNet).
If anything, it’s the Apps which have to change, not /e/. Question is, how e.g. Banking Apps can then ensure the integrity and safety of the device for banking. Doing it the Google way is the easy way for App developers, in general.
The Google ecosystem is working well for App developers and most users. /e/ is made for those who want to leave that ecosystem because they don’t feel this way.
With the help of microG (which is included in /e/) you might be able to still tap into this ecosystem to get some (by far not all) Google-dependent Apps running for a while for your own convenience, but that’s it. Else you can try to find existing Google-independent Apps for your use cases, or you can try to get the developers of Apps to build Google-independent versions and make them available outside of the Play Store (Good luck with that!), or you can try to use a website instead of an App (if you’re lucky it’s PWA-enabled and feels like an App), or you can try to change your use cases to not rely on Apps which don’t work outside the Google ecosystem.
/e/ can’t do magic.
Just use the stock Android OS of your device without a Google account (you can skip this step in the initial setup), uninstall every Google stuff you can uninstall without crippling functionality, and browse through all the settings to make some sensible Google-related choices.
Here’s an (old) example of this for the Fairphone 3. Things definitely will differ for recent versions of Fairphone OS or for other devices, so some research will be necessary.