I don't doubt you used Googles app store to access the banks app (as would I), but it's not because of something Google forces you to do. It's because your bank put it there, and it's a very a convenient service for both you and your bank. Unlike the iPhone environment the bank had a choice in using the app store. They could have you side load it, or they could put it in an alternate app store, or hell they could open source it and use FDroid's app store.
It seems to me there is very little stopping there being a whole pile of competing Android app stores out there. Technically there's nothing stopping it in fact, as the existence of FDroid illustrates. It's purely a matter of convenience - which is the same thing that drives Chrome's dominance on Android despite there being better browsers available for free. The play store app is pre-installed and is almost a one stop stop for all the apps you could possibly want, so who is going to bother loading another app store?
Turns out that edge in convenience is enough to create an effective monopoly in app stores, for most people anyway.