It has little to do with Americans being violent. It comes down to population density. The US has a ton of places without the population density for pick pocketing to be effective.
People forget that a lot of the US is almost uninhabited.
Plus, personal space is a pretty big deal in most of the States. If you're too close, I'm not watching for pickpocketing. I'm too busy working out what the hell is going on in a panic because something is already wrong.
Sure we're a bit violent, but we're friendly first.
I'll say that I've never been to Europe, but I've been out and about in central and South America and as far as I know I've never run into a pickpocket. Maybe it's just a European thing.