I was watching Martha Stewart on PBS a couple years ago and saw her do the same thing. I skip the first step of separating the head into cloves and just shake away. It totally works and is one of the best kitchen/life hacks ever.
I have to admit that I've been lazy lately and have been using the pre-cut/chopped jarred garlic. Not nearly as good as fresh
but a lot faster when I'm trying to throw dinner together.
I find that unless the garlic is super fresh, I have to shake it with the force of a jackhammer to get all the cloves peeled. What works best for me is to separate the cloves first, then individually squeeze the two ends of each clove in to pop the skin off.