Although we may always need apps for use on smaller screens, I think Trip Hawkins is ultimately correct. If we move to a cross-device world, where diversity in operating systems reigns, then the one constant denominator will most likely be the browser. And in that browser, the apps would be consistent no matter what OS is used on any screen we use in our digital lifestyle.
That means that developers need to be able to create great apps on OS platforms, as well as the browser. Steve Jobs has actually pushed this scenario too. Part of his decision for not supporting Flash was because he feels that HTML5 and future versions will be robust enough to deliver complete audio, video, and enhanced, graphics-based apps. I have no doubt that even though Apple will push its apps platforms, it will simultaneously deliver a more powerful browser app SDK in the future.