[When I was young] starting pitchers went more than five innings, when the closer was actually the starting pitcher much of the time. Could you ever have imagined a manager taking out Koufax, Drysdale, Gibson or Seaver in the seventh inning?
Average number of innings pitched in games which they started:
So, yeah, actually I can imagine a manager taking these guys out in the seventh pretty darn often.
UPDATE: Click the comments to see Roger Moore's fabulous -- dramatically more detailed -- take on this than mine.