I fight squarish so the changing of the stance is not as big a deal as you might think.
You are also correct that I run the risk of running into a punch. But then again that is a big risk for any style that revolves around mobility. Slipping that cross can be great until you misjudge it and slip into a hook. This is countered to a point by making your movement more versatile and thus less predictable. If your opponent can't hit you where you are and has trouble picking where you are going to be then it becomes very difficult for them to make you run into that hit.
As for the increasing the power of the punch, it is like running your punch into your opponent. If you spring your body weight in the same direction as your punch at the point of contact then its all good. The hindrance I previously discussed becomes the strength of the footwork. You can increase the power of the hit by increasing the amount of body weight thrown into the punch (e.g. sitting into punch, step in the direction etc). Sitting into your punch and stepping into the punch both use similar principles.
Also don't confuse my use of this type of footwork as my only footwork. I use traditional footwork too. I pivot and step with my lead foot for jabs etc. It is just another tool for my arsenal. I have quite a few different jabs. My hardest power jab is when I step forward and out with my rear right foot. It is almost as hard as my right cross. This also seemes to work best when my opponent is coming at me. I add my slip and make them run into my power jab. I can then peel off to the side and pivot out at a new angle or step back in with my left foot whilst firing a right punch/kick.