The only things I can find about app stores in the paper by Google[0] run directly counter to your idea:
> Android explicitly supports installation of apps from arbitrary sources, which led to the development of different app stores and the existence of apps outside of Google Play.
And this:
> Both users and developers are part of an open ecosystem that is not limited to a single application store. Central vetting of developers or registration of users is not required.
And as far as signing goes:
> In order to ensure that it is the app developer and not another party that is consenting, applications are signed by the developer. This prevents third parties — including the app store — from replacing or removing code or resources in order to change the app’s intended behavior