More than that, the Hall criteria for closers is pretty - well high is not the right word, but specific.
Early guys have gotten love, Gossage, Sutter, Fingers (and Sutter was a very shaky pick). Since it has become a 9th inning job, the bar has gone up a lot higher. Eck and Smoltz got in, but also had a lot of good starting years to back it up. Papelbon right now is in the Lee Smith, Jeff Reardon soup - which is not getting a sniff right now. Really outside of Rivera and maybe Trevor Hoffman, it will be very hard to make the Hall doing that job.