It was said to be Eck that changed how teams used relievers. Eck was used lighter than most closers in the late 80's, early 90's and someone (whether correct or not I have no idea) established that the relievers who had more consistent ERA's (the indicator at the time) were pitching closer to 1 IP per outing and the guys that seemed to blow up (Dibble, Montgomery, Henneman, Assenmacher come to mind) pitched closer to 100 IP's.
How much would another 25 or so innings change Brad Brach's effectiveness? Hurt him longer term? I do agree that there are only a handful of guys that could be difference makers being 2 inning relievers throughout the season.