Morris got popular in the same way that Scott McClellan did with liberals: he was an insider who turned on his boss. If conservatives get tossed aside he’ll be right back on CNN like Fox never existed.
Morris was fired because he became an embarrassment to Clinton; but at least, unlike McClellan, Dick had been involved in the Clinton decision making process and could offer real insight into Clinton’s actions and thinking. Unfortunately Dick’s only skill is at pandering and he always tries to tell people what he thinks they want to hear, not a trait that helps a talking head have anything worth hearing.