JASP, that's a unique definition of park and ride, the total absence of movement idea. I've never heard someone suggest high edge angle turns can also be considered park and ride. The low edge angle version I described above is the most common version I've heard over the years from instructors and coaches. This is what I'm talking about when I say there's much misunderstanding out there about the term. Seems everyone has a different twist in their personal definition of park and ride, and like you have, find a way to deem it a negative event.
You're right that it takes some form of movement during a turn, even when edge angle remains constant for a period of time. As we proceed around the turn, the forces acting on our body continuously vary because of our constantly changing speed and relationship with gravity. So yes, to maintain the desired state of balance, and the cleanest arc, while absorbing undulating terrain, a continuous series of micro management movements need to be employed. Good skiers do those micro movements without even thinking about it, and usually they're so slight they can't be seen by the naked eye. Only how the skis interact with the snow indicate they've happened.
What you describe, a total void of movement, Frankenstein type skiing, is something I seldom see. In lesser skilled skiers, where you would most expect to see it take place, the more common thing to see is wrong movements. I do see something I coin DOG IN A BATHTUB skiing, where the skier remains very stiff as they ski, but even in that some movements do take place. I would think skiing with absolutely no movement would be very hard for a person to pull off, requiring a strong commitment to overcome the human survival impulse. Something's usually going to be moving as a skier's lack of proper movement causes them to lose balance, and their skis to skip across the snow.