I suppose there is no wrong way to do anything once you can do it well. For me, there is no way I could alternate pick as fast with my arm as opposed to my wrist - it's a combination of body mechanics and time spent practicing a set technique at the end of the day.

Try the following exercise to see which really is best for you: use your current technique on one string unfretted tp pick as fast as possible up and down rhythmically (123,123,123) with the accent on the 1 of each set of triplets. Then try the same up down stroke at max speed using your wrist only. Try a number of variants until you establish which give you the fastest pikcing with the most accurate rhythm. Whichever works best then stick with it and work from there. Everyone is built differently and quite often people start off with an 'incorrect' technique but because they practice it so much it works amazingly for them. Once you get to a certain stage it becames almost impossible to change your technique. For example, anyone who has been playing for a coupe of years who tries to pick like Michael Angelo will quickly find themselves sounding like a beginner again.

Picking speed is not something you pick up over night, it takes years to get to your top speed, the big trick is to punctuate the rhythm with accents - this helps you to feel the rhythm and establish a groove (important if you are chopping the same note for 32 picks for example). Hope that helps.