That's not an easy question to answer because the "closer" is a relatively recent invention in baseball. The "closer" has only been around for about 20 years and really started with Tony LaRussa and Dennis Eckersley. Back in the "old days" starters were expected to start and finish. If they didn't, you brought in a relief pitcher. He came in during a jam, cleaned up the mess, and finished the game. Teams did not have a bullpen full of "specialists."
If I was a manager and my team was in a jam, I would want Rollie Fingers or Goose Gossage coming out of the bullpen. They were the fireman, the set-up guy, and the closer all rolled into one. And they could give you two or three innings per appearance if you needed it.