As pitchers get older, it becomes more important to develop off-speed pitches. Coaches can respectfully disagree with which off-speed pitch should be developed first (I believe a change-up should always come before a curve ball) but it is clear that the overwhelming amount of pitchers will no longer be able to simply throw a fast ball past most hitters when they reach certain levels.
That being said, some pitchers fall in love with their off-speed pitches too much and actually make it easier for some hitters. If a pitcher has average velocity for his level, he may struggle with the better hitters on the opposing side if he just throws a fast ball. This is because better hitters are "better" in part because of their ability to time and hit average fast balls. But the hitters farther down the order are, in part, probably there because of their inability to hit an average fast ball.
It makes perfect sense to include off-speed pitches in a pitcher's strategy when facing the other team's better hitters. Doing so forces them to think of something other than a fast ball which makes it less likely they will be able to be on-time when they do get a fast ball. Of course, these good hitters only really have to worry about an off-speed pitch if it can be thrown in or near the strike zone.
Hitters down in the order may, in fact, welcome off-speed pitches because the slower speed of a change-up or curve ball better matches their slower bat speed. In this case, a pitcher may be doing them a favor by throwing a slower pitch. "Speeding up a hitter's bat" is a phrase in baseball which means just that.
More awareness of each individual hitter in terms of strengths and weaknesses will allow a pitcher to tailor a separate strategy for each one and can help to eliminate the mistake of "speeding up a hitter's bat."
