That makes it possible for a UI design where the user can press a button and say "don't surf this site anonymously" with the default being a new random session-id for all other sites.
That will make tracking and correlation of webusage much harder, which I really don't see a downside to.
Deflate is bad on its own, it is a DoS amplifier and it makes the job of load-balancers much more resource intensive, because they have to retain compression state for all connections and spend CPU and memory on the inflation.
The server is perfectly justified in customizing content, and we have a header for saying that is the case: Cache-Control.
The problem with cookies is that they disable caching of everything on the site, including favicon.ico and there is nothing the server can do about it, because the cookies are sent on all requests.
Javascript will also have access to the session-id.