Google doesn't have the technical ability to "turn off all the self-update stuff", if you mean preventing non-store apps from updating themselves by downloading and installing apks. The worst thing they can try doing is bullying the users into uninstalling the app through Google Play Protect.
I'm not deep enough in the Android ecosystem to understand all the details. I've only had the misfortune of trying to get a (very portably-written) golang application to run in the environment, and hitting roadblock after roadblock.
I guess my overall point is that Google is motivated to have complete control over Android app distribution, and they'll plug as many of the types of holes you're talking about as they can get away with.
