While it's always hard to find HBD's equivalent of an Eckersley, it is not that hard to find pitchers who will perform acceptably in the closer role.
There having been lots of seasons when I didn't have a great closer, I discovered pitchers I otherwise wanted to use as SuA's had better numbers as closers. I came to the conclusion that the less time a pitcher is on the mound, the less chance he has of being exposed, so to speak. Perhaps the closer role minimizes in-game fatigue.