How does this eliminate the need for cookies (I'm assuming you mean web browser cookies)? No matter how much you can save on the server side, HTTP is stateless and you need some piece of data coming from the client to indicate that this request is tied to a previous request (or series of requests). Even if you could save the application state of every Apache child (assuming Apache) for every simultaneous user, there is still no way to figure out which one to use for the next request.
-- More people are killed every year by pigs than by sharks, which shows you how good we are at evaluating risk. -- Bruce Schneier