I think you have the description of that pitch reversed. That pitch wasn't developed by those guys with arm troubles. It's what actually shortened the careers of those pitchers. That's why you see more guys today who throw sliders and cut fastballs instead of splitters.
Mariano Rivera was the master of the cut fastball. He learned it by mistake in the bullpen one day while fiddling around with his delivery, and he rode it to a long career as the best closer in the game.
I don’t think I have the description reversed in Sutter’s case. He had arm surgery after being signed by the Cubs and his old pitches stopped working. He learned his signature new pitch from an instructor in the minor leagues, to whom he’d return for years whenever he was off. Early in his major league career the Cubs made a big deal about how the pitch had saved his career. He had shoulder problems late in his career, after the Cards were smart enough to trade to the Braves. Perhaps they were from all the splitters.