The server initiated Cookie header is superior to a Request-Id in several ways and has much greater functionality. Dan Connoly's suggestion of using an authentication request to signal that something like a Request-Id is needed seems like a kludge. It is also not as efficient as Cookies.
Cookies also make it impossible to corelate log data from different servers.
The cookie from one server will never be sent to another. This is a serious problem with session-id. I believe that this is the current Netscape behavior, documentation to the contrary notwithstanding. Yes, and I personally find this objectionable. It is the reason that I have never been beyond the front door of Hotwired.