I think you might want to question your assumptions. The reason you want to do everything in the browser is probably twofold:
1) Inertia (that's the way I've been doing it for a decade, dagnammit), and
2) It's an easier context-switch. Rather than go back to the home screen, swipe over to the next app, and tap it, you just just type in the first few letters of the url, then select the site you want to go to from the drop down list.
But
1) Has had pretty poor predictive value in the last few years, and there's no reason to suggest it'll improve. Our entire industry is built around disrupting inertia.
2) Is ripe for disruption. At the end of the day, when you get right down to it, entering the first few letters of a url then selecting the correct site is both an arbitrary, and not particularly optimized workflow. The fact that we are used to it does not mean there aren't far better systems out there. Sure, Chrome on my MBP has learned to take me to my top 10 sites with cmd-l -> $url[0] -> enter, but my mom needs her buttons on the bookmark bar. I tried to remove the titles, thinking she could easily recognize the favicons, but no dice. She needs a start menu-like interface.
Similarly, I was on the bus with my friend, browsing reddit. He buys tons of apps for his iPhone, and he looks at my screen and says, "is their mobile app free?" I said, "well, yes, but most people just browse to reddit.com/.compact". he stared at me in disbelief. Why would you use the browser if you can have an app?
For those of us who live and breath the Internet, it seems only natural that a write-once-run-anywhere website would be more appealing than having to download some stupid app from some stupid store, type in your password, then have to remember which home screen it's on, etc. For those who use the internet as casual content consumers, however, apps take a lot of the frustration out of it. Want to read the economist? Tap the economist button. That's it. Want to watch a youtube video? Tap the youtube button. Need directions? Tap the map button.
For the casual user, these workflows are far more intuitive. My friend, who has spent hundreds of dollars in the App Store, rarely uses the browser on his phone. He uses the Plenty of Fish app, the Chive app, etc. For most non-technical users, this just makes sense. It might seem annoying to us, but we are not the largest market segment by far.
Now it might be that we'll see mobile web sites with a light wrapper disguised as apps; perhaps cache and a link that opens in the browser. Maybe we'll see native support for the kinds of things that are typically done in the browser. But, crucially, what I don't think we'll see is the dominance of mobile web over native clients. For the vast majority of people out there, I think they just want the app.