but I can guarantee that his primary objective is *not* to turn your hand purple
Naturally I agree, but the principles learned through somebody grabbing your hand hard and grabbing your hair hard, or your arms hard or whatever are the same. Otherwise why practice katate-dori at all, it wouldn't make sense.
You should be able to move whatever the hold or attack, or even better before you are grabbed or struck. The principle still applies before the event as it does once you are grabbed, tense up and you wont be able to move, remain calm, focused and relaxed and you will see that they don't really have you at all.