Setting up a chat so that each client talks with every other client would be difficult (read nearly impossible). Think about perlmonks.org. During the day, there can be over 60 people logged into the site plus any number of people visiting the site from all over the world. Now imagine if someone entered something in the chatterbox. How would my browser know what browsers to send the message to?
While this is a somewhat convoluted example, how would the various clients know what other clients are out there without connecting to some kind of server.