The advantage I find to archiving messages is just a slight psychological boost. When the inbox is empty, I know I have nothing to do. If I have <20 emails (I always try to keep these inboxes under 20), I can see everything I have to do. As I work my way through the list, it's obvious visual feedback that I'm making progress. Just little things that I feel slightly improve my experience.
Although this only works because I have my other massive "online" inbox :D