> If you made an "app browser" that allowed better searching (type the first letter and the app appears --- tap to open it)

The iPhone has this. Just swipe right on the home screen.

> and easy navigation between apps

On the iPhone, double tap the home button and you get a taskbar of your running apps.

> Why couldn't Apple allow mobile web apps to be sold in the app store? It's an icon that opens a web page. It could be as simple as that.

Phonegap allows you to bundle a html/javascript webapp as a native iPhone application. There are even hooks in there to access the camera, gps, etc.