Because its bad for your elbow in the long run, ie. tendonitis.

At first, using your arm is really easy cause is simple, but using your wrist to alternate pick will help you with acuraccy aswell as economy pickings. If you ever plan to do high speed string skipping runs, your arm will be to slow and cumbersome to move those couple inches between strings.

Many people tend to use their arm cause you automatically can tremolo pick, and tend to not use the wrist cause its harder. If you practice using your wrist, you will eventually get faster than you ever have with your entire arm. Then again, dont think about stationing your arm too much cause even when you move your wrist independently, your arm does naturally move - thats ok. What you dont want is your elbow to tense up to where you can see that tendon from your tricep bulging our of your arm - thats bad. It also cause fatigue and you will only be able to speed pick for a certain amount of time before you get tired.