The invention of the late inning closer is sometimes attributed to Tony Larussa when he moved Dennis Eckersley into the bullpen. But late inning closers were already pretty common before then. Older Twins fans will remember Ron Davis struggles in that role in the early 1980's before Dennis Eckersley ever saved his first game. What Larussa did show was that by limiting a good pitcher to one inning at a time you could get outstanding results.
There are several reasons this works. Fans, especially statistically oriented ones, look at pitches thrown, batters faced or "innings pitched" to evaluate pitchers work loads. They don't pay much attention to the work involved in getting warmed up. But warming up is not inconsequential. And the effect is probably not linear. After a pitcher has warmed up once and pitched briefly, warming up a second time probably adds more to the strain on arm and body than the first time around. Of course there are a lot of factors that will influence that including the weather, how much they pitch, how long they are on the bench and the pitcher's own body. But it is important to remember that a closer who pitches to even one batter in the 8th, or even warms up in preparation to pitching in the 8th, is getting a lot more extra work than that brief appearance in the game might indicate.
So there are physical implications to using your closer starting in the 8th. But, perhaps more important, is the psychological impact. Coming into the game with the idea that when you leave the mound it will be over is a very different task than coming into the game and knowing you will have to come back out again the next inning. It means that instead of putting everything into a single pitch in a critical situation, the pitcher needs to consider how that might effect his performance the next inning. Suddenly the lights out closer in to finish the game, becomes a setup guy trying to eat up innings. Worse, unlike the real setup guys, there is no one who is going to come to his rescue if he can't get the job done.
While I don't think you can draw a firm conclusion that Capps struggles are a result of being used in the 8th. It may be that was the situation in three of his four blown saves is just a coincidence. But there are reasons Larussa's use of Eckersley has been mimicked ever since. It seems to work much better than having your closer be his own setup main.