"What problem does a web application solve that a desktop GUI frontend to a network server does not?"

Browsers are huge beasts. If, looking at a single application, one could take away from the browser all the things that a particular application does not need, what would that application's size be? Given good UI libraries, perhaps a million times smaller?

Of course, it's the good old "Worse is better" again. I haven't lost hope, though. I'm sure we can come up with something better than the browser.

edit As an example of something vastly better that already exists in a stable form: http://www.rebol.com/docs/easy-vid.html