Google does not notarise apps outside of the Play Store on Android, so, no, they will not do exactly that.

My fav App Store on a fresh Android is Chrome, because you can use Chrome to install any other app store, or any app directly from any website.

On iOS, there's no such alternative.

In fact, on iOS, you cannot install ANY app at all until you login into an Apple Account. In fact, even some pre-installed premium apps (Pages, Numbers, Keynote) on iOS cannot be used before you login into an Apple Account.

By comparison, Chrome lets you install any app from any website without providing any identifying information, preserving you privacy. It's very easy to dismiss the login screens when setting up a new Android device, too; something that Apple also makes far more difficult on iOS.

Google can and will do exactly the same thing on android in a year when they implement the functionality.