I don't disagree with your overall desire, it would be nice, and I agree that it seems like Apple is probably moving in this direction. Trouble is I don't see how they could really hit what you're describing without confusion. The Fire TV is probably a bad example of this, because nobody is going to accidentally buy a Fire TV app on an iPad thinking that it's an iPad app.
Well, okay, some people might. But it's not likely. To be sure there was no confusion, Apple would almost have to do something like what they do with the iTunes stores, where the interface for buying music vs. the interface for buying movies, while in the same app, are in different sections and are totally different colors. And from what you're describing, that sounds like more segregation of the content than what you want.
But yeah, if they were to add a tvOS app to iOS that I could use to buy apps and push them for download on my Apple TV, that'd be fantastic. The dream of getting the tvOS apps all mixed in with the iOS apps seems problematic at best to me.