The app stores you mentioned are inextricably to their respective operating systems. The problems with the Play Store are a compromise I'm willing to deal with so I can easily install apps using alternative app stores or none at all.
Really?
https://play.google.com/intl/en_us/about/developer-distribut...
> (4.5) Alternative Stores. You may not use Google Play to distribute or make available any Product which has a purpose that facilitates the distribution of software applications and games for use on Android devices outside of Google Play.
You have no chance of bootstrapping an alternative store outside of Google Play. Sideloading APKs is not how users get software on Android. Amazon failed hard with their attempt, and they pumped tons of money into it by paying developers to give away their apps for free; that, and they shipped hardware that has their store preloaded. Still didn't even make a dent.