Please tell me how I can run my own version of Android on my Samsung phone that doesn't phone home to Google or Samsung, while still being able to run my banking apps.
If the duopoly hadn't trained users so well to rely on app stores for everything, banks probably would've invested more in web interfaces. At one point, the Bank of America website was the only access point for Windows Phone, but it was good enough for my needs and helped supported a little more diversity.
You can generally sideload whatever you want on Android.
But people will ALWAYS point out the edge cases such as banking apps not working on custom firmware/rooted devices, and somehow that makes Android very bad and very walled garden.