Not every 0-2 is the same. Runner at 2nd, with two outs. A great hitter at the plate, pitcher throws a quality FB down and away for called strike one. Throws a second FB dead red and gets fouled back, strike 2. A hanging curveball or CU up in the zone is trouble, and pitcher knows it. So, he over compensates and spikes a curve 5 feet short. Comes back with a low and away FB a foot off the plate 2-2. Now he has to realize a hit is worse than a walk. Throws quality a CU low that locks up the hitter, the hitter takes, called ball 3, 3-2. Throws a quality FB that is fouled off. FB up out of the zone ball 4.
With age, experience, confidence, and command of secondary pitches, that 0-2 curveball needs to move towards the black of the plate.