Well, if you're looking at it with an anarchist mindset (and most of American-produced Shadowrun has been without that for about fifteen years now), then chaos magic would not only be outside tradition, but it would actually throw off tradition- so if you did a spell a certain way, and saw a coyote shaman casting it the same way, you'd probably have to find a new way to do it.
I was just thinking, chaos magic as you described it (which I really liked, by the way), would be very powerful- almost overpowered, because a brand new character would be able to cast any spell they could think of, with no maximum power. A good handicap for that, I was thinking, is that chaos mages wouldn't be able to initiate, so higher-level magic would be beyond them.
But it was just a thought.
-kv