Dealing with the security and privacy aspects of those would be enough to get near the complexity of an OS. And to note...looking at the facebook app for instance, being native doesn't seem to be a protection from bloat, it will there either way.
On the web as a static thing, sure 80% of the web is fine as a static information. The 20% on the other hand are things we care a lot about, and I personally hate the "why don't you install our app?" prompt on every damn site. Reddit is the poster child of this, and god no I don't want their native app.
To each their own I guess.