The truth of the matter, 'closers' generally have short careers as such. There very few like Rivera that can be effective over a long period of the time. I'd say the average lifespan of the a closer is about 3-4 years. Set up guys and closers are basically 'flavor of the day' types...who is hot and/or who the manager can trust at that present time. While true you want players that believe they can get it done, but you have to prove it. Otherwise..... Like Joe Girardi basically said, his job was to use the players in a way that gives the team the best chance to win. So if there is someone better or they trust more, you're riding the pine. That is the way it's always been.
As for Papelbon, he's always been a cry baby. Very likely why Boston management and players weren't too sad when he left. Time for Washington, to cut him loose and let him be another team's problem.