They could offer a Play Services API that allows app stores to update apps which the user previously installed through them. As Play Services already has an AP

They could offer a Play Services API that allows app stores to update apps which the user previously installed through them. As Play Services already has an API and the permissions to replace installed apps (although this API is currently only available to the Google Play Store), and as Android already tracks from where an app was installed, this would be easily possible. But knowing Google, they won’t allow this.