I think at some point, we could feasibly reach a point in development where the website could also be the native app. In that case, the app store is essentially a self-contained browser, running the mobile site.

The reality of that situation right now is not pleasant. Some apps already do this (looking at you Wells Fargo) and the experience ranges from awful to passably ok.

Ignoring all of the technical hurdles for the moment, we should also stop to consider some of the real world implications of native apps. Does my calculator really need an internet connection? Couldn't I play flappy bird while in airplane mode? Even apps which depend on an internet connection to function (like an RSS reader) can still serve some functionality out of their caches when offline. But if the app itself is delivered as a mobile web page, those features won't exist.