They also used him to get rid of a couple of elements on the show they didn't like: The fish in Picard's ready room that Patrick didn't want (He thought Picard keeping a captive animal was inappropriate)
Actually, the fish was still in the ready room for the rest of the series after Chain of Command. In Genesis, Caveman Riker can be seen beating on the auquarium. Indeed, we even see the empty aquarium in the wreckage in Generations, suggesting Livingston didn't make it.
In regards ot Jellico, I wonder if maybe the resaon so much of fandom is so hard on him is because Ronny Cox has been typecast as spineless bastard (most notably with his role of Senator Kinsey in Stargate) and when people see Jellico they involuntarily see the other roles he's noted for?