Iselin and Spectorsky wrote about the gliding wedge back in the 1940's. Their advice is as timely today as it was way back then. The analogy they used about a pound of butter and a knife speaks directly about edge angles. Too little edge angle and the leading edge of the skidding knife digs into the surface of the butter. Too much and the knife scrapes off a layer of butter and as butter builds up under the knife, the knife will want to move along it's edge instead of sideways across the surface of the butter. The PSIA test maneuver echoes this idea and can be seen in the requirement of opposing edge usage and both skis skidding throughout the maneuver.
As far as the weight shifting to the outside ski, well that already happens as the skis turn and the body tries to go straight. Again since it's already occurring and occurring at a sufficient rate for the intended turn, why would we want add more? It really goes back to the idea that any move done in excess is just that.
This brings up a third and IMO even more important thought. Patience and touch are often the hardest thing to teach. Especially down at the level where we would be teaching a gliding wedge. But that is exactly what it takes to do that test maneuver well. If you struggle to do this maneuver, back off the effort and explore letting the skis do more of the work. As far as how that relates to parallel turns, well in most cases wedges occur when we try to do parallel turns at such a slow speed. But we could argue about this for another seventy years and still not convince everyone.