Though web developers only worry about the rendering engine, users mostly care about the chrome. Tabbed browsing, the search bar, well organised history and favourites, and full page zoom controls are recent chrome innovations critical to improving the user experience.
Instead, they use their own user interface frameworks - Mozilla, for example, has a markup language called XUL. If you look at XUL, it's pretty much a non-standard competitor for HTML5. It's been great for Mozilla until now, of course, but what's the point once you have HTML5 itself? Why maintain code for two separate markup languages?
Using HTML5 to program the browser chrome would make extensions, such as the popular Firefox extensions or even single-use applications like Prism, vastly easier to develop. They would also simplify browser code and reduce its footprint.
As HTML5 gets stronger support by browsers, we may see a new tipping point, where HTML becomes the default user interface framework even for local client applications. We'll see an HTML browser chrome in the next few years.