The problem is that every app will have to be verified to be installed on Android, not only the software that is published on the Play Store. This also touches alternative stores like F-Droid. To make an example, is like blocking apps in Windows that are from "an unkwnown source". If you want to develop apps on Android, you will have to be recognized from Google first.
Android is no longer an open platform in the way we used to think of.