Being no pucker factor in HBD, closers are pretty much a waste of time. Even with a lights out low stamina/durability guy, I usually look to trade them if I can, as other owners will put more value in a "closer" than I will so I can get a better return for my team.
Closers are stupid in a sim game because of situations like this: Hardball Dynasty – Fantasy Baseball Sim Games - Player Profile: Luis Pena
This guy is a career closer in one of my worlds, and he has an outstanding amount of saves. Big deal, he should have been a career SuA, giving 150 innings a year, instead of the lights out 40 he has been giving. His owner has been sucking up the additional 100 innings with a lesser arm, and it is costing him games.