Also, falls, pops, and poor jumps should play a role in PCS. You can interpret the PCS guidelines anyway you want I suppose (most judges do), but go watch an awful performance live and see if a good step sequence compensates. It dramatically affects "projection" and the "emotional / intellectual involvement" of the skater (you can almost see Carolina's impetus come crashing down as she fell on the triple toeloop) and it invariably messes up your timing with the music. Additionally, while you are regaining your composure coming out of a fall or pop, you are missing some choreography. Those are key components of performance, interpretation, and choreography. I'm not convinced you really believe popped jumps and falls don't deserve to be taken away from PCS. If someone popped 5 of their 7 jumps, would you say they deserve an 80 in PCS because they are good at step sequences and blowing kisses?
PCS has absolutely nothing to do with your numbers of successful jumps. You can pop all your jumps and still deserve sky-high PCs. There seems to be the fixated idea of some members on this forum that TES are PCS are directly linked and when you get high TES, you also deserve high PCS and when you make mistakes, your PCS should go down which is not how CoP is supposed to be used. Only when your technical mistakes affect the presention of the program, the PCS should be affected.
Also, she had errors in 4 elements (I suppose you could be generous and argue the almost-tripped out of a spin wasn't an error). There are 12 elements in total. 4/12 = 1/3. voila.
You said her mistakes were in 1/3 of the program. Now you are talking about the number of technical elements which is definitely not the same. One could argue that in Carolina's case her mistakes were not very disruptive, she got good back into the program after the fall very quickly and the popped jumps were only noticable for a few seconds. I agree those errors affected P/E to some degree but her skating skills did not get worse because of them, she still skated mostly in time to the music and missed only a minimal amount choregraphy of the 4-minute-program.