You had to side-load it, right? That's the point, you can't install another App Store without side-loading, which is riskier than third-party app stores.
And of course other stores aren't on Google Play That would be like Walmat allowing a Bestbuy to setup inside its walls
The problem with you analogy is that Walmart (Google Play in your analogy) is the only store where you can "legally" shop. Every other store is considered "under the table" and "use at your own risk"--kind of like buying from the guy on the street corner in front of Walmart.
A better analogy for what I would like Google Play to be, is a shopping mall. Lots of stores under one roof.