I believe id is using the web browser/plugin for a couple of reasons. First, they want to efficiently simplify the updating system. Once you login, it always checks and updates files in the plugin to make sure they're up to date. It will also update in-game ads use. Today, this is often done by yet another program to run in the background of your computer (jusched.exe comes to mind).
The second purpose is to unify the user experience. Since Quake Live is designed to be an on-line "community", they want the forums, chat boxes, user profiles/stats, and game searches to be in a single interface. Even if you play the game in full-screen, once your match is completed it takes you back to the "lobby" which is just a nice web page, complete with ads and instant updates.
It does seem silly on the face of it to think that the plugin is large enough to be a stand-alone download, but there are some legitimate business and technological reasons for making it the way they did.