I subscribe to Lefty's logic on this one. If you're right handed your right foot should be back. This, like Juro said, increases the range of motion available to your casting arm while traveling on a level path. The logic goes something like this, as I understand it: The rod and forearm are one. What the elbow does, the thumb does (more or less), what the thumb does the tip of the rod does, and what that does, the line does. If your elbow travels in an arc, so will the line, which wastes energy. However, if you can keep your elbow traveling in a straight line parallel to the ground, you can move your arm as far back and forward as you want, which gives you more room to load the rod.
Of course, if your bend your wrist, you break this arm-rod connection and the whole deal's off.
If, however, you cast 'squared up', like your shooting a basket, then you can only move your arm so far back before you have to turn your body or lift your elbow. This can be difficult to get the hang of without ruining the loop, particularly for longer casts. Placing your dominant foot forward makes this even worse.
Another thing to consider, the last two stances lead to too much shoulder work which looks like rotator cuff problems in the making. Fly casting can be hard on the body, like any repetitive motion. If you depend too much on one joint - shoulder, elbow, or (god forbid) wrist, you'll stress those joints. However, the side arm stance (your #3) lets the caster distribute the casting motions throughout several joints and even encorporate a rocking motion with the body. In a way it distributes the work load easier. I find that I'm working less to cast farther now that I've really begun to focus on proper stance and arm motion.