OK, I read it -- and
tried to understand it!

I'll just throw out a general impression, and hopefully all you more knowledgeable folks can run with the ball!
If I've read this correctly, it seems that one of Schaeffer's main concerns is that CoP will have the effect of devaluing the Presentation side of the Technical/Presentation judging equation, and he offers some data to support this. Most startling, it seems that the proportion of raw marks derived from "presentation" dipped well below those derived from "technical" even in the Long Program, negating the "spirit" of the 6.0 system.
I have no comment on what the implications are for the sport if this proves over time to be true, but I do have some sense of why the presentation scores are perhaps lower than expected.
While there were always objective criteria behind the Presentation Mark, it seems to me that under the 6.0 system there was also, for better or worse, an allowance for the subjective as well. For the "whole is greater than the sum of it's parts" effect. By dividing the Presentation Mark into the 5 components of Skating Skills, Transitions, Interpretation, Choreography and Performance/Execution, each exhaustively detailed, the overall Presentation Mark has become far more objectively based. We all know that certain top skaters, even on their worst nights, never received presentation marks lower than 5.6 or so, and for a great skate were practically guaranteed 5.8s and 5.9s. On a 10 point scale, this would translate to a range of maybe 9.3 - 9.9 (or 10!) per component, and I frankly don't see that happening. Take Michelle -- even if she were to receive high marks for Skating Skills, Interpretation and Performance/Execution, it is unlikely she would do as well (based on past performances) for Transitions and Choreography. By objectifying the criteria for awarding these marks, judges are precluded from bestowing the highest possible mark based on the emotional "wow" factor -- e.g. "She made me cry with that performance, and I haven't cried for any performance since (x) won (yz); I gave that performance a 6.0 so I'm giving this one a 6.0 too!" The "wow" factor could still come into play in the awarding of points for Interpretation and Performance/Execution, but it would be far less likely to elevate the combined Presentation Total.
The good part of this, IMO, is that reputation should begin to count for less. It always frustrated me no end seeing skaters getting inflated presentation marks for impersonating a Zamboni, and looking miserable in the process! But I also do feel that there is a certain magic that can happen on the ice that sometimes transcends it's purely objective elements.