Sometimes I do wind up in full sprint. But if your point is that quickness is more important for court coverage that speed, I'd say you're correct. An experienced player who always gets a good jump on the ball never seems to have to hurry to get to the ball. Beginners usually don't move until the ball has crossed the net and even taken its first bounce. Even a track star beginner will struggle to cover the court while playing a pusher.
The shortest sprint in the Olympics is the 100 meter dash, but from the center of the baseline to the sideline is only 9 yards. Look at the mathematics, it's more about taking a few quick steps than all out running.