I think the various Mozilla projects actually do have facilities for this, and that some significant portion of the chrome is done this way.
Where browser UIs aren't done this way, though, I suspect it's because the APIs are for components that aren't markup based -- you write the software for the platform with the APIs it provides, or (as I believe Mozilla has done) you write your own platform on top of something else.
I think the real question to ask yourself is -- if the conventional patterns of the desktop API that we'd more or less laid down by the mid 90s were so generally awesome, why didn't some universal client based on them take off instead of the web?
It's not as if we didn't have network aware desktop-style clients at the time...
I think we are asking opposite questions - if web based UI's are so awesome and have no caveats attached for display based apps then why are browsers not written using HTML, CSS and JS ? I am asking this question because I know at least one person from mozilla has replied to this thread.
"why didn't some universal client based on them take off instead of the web?"
Because you had several companies all fighting to have their desktop platform be the standard. The web slipped in the back door because nobody felt threatened by a hyperlink document publishing system. As such, it was the only platform that was available everywhere. Worse is better.
Interestingly, the web is starting to adopt the old desktop model. If you look at many of the emerging frameworks for web development (talking client side here), they all seem to be loosely based on the work of OpenStep.
It is actually a really great question posed by dman. If the web is suitable for applications, the browser chrome should be one of those such applications.