Thank you! That one makes the most sense of any of the ones I've seen.
As for why to use a PCO, it's oftentimes a matter of preference. I'm about to start two different afghans and they will both have PCO so that I can easily join the squares (I don't mind kitchener, and definitely prefer it to seaming), and so that when I'm done with them I can easily add a border without having to pick up stitches along all 4 sides. Picking up stitches tends to be a bit messier, IMO.
It also makes it possible to do something like the bottom of a flat-bottomed bag... if you pick up stitches along 3 sides, they will never match the fourth side. Instead start with a PCO, so that the sides opposite each other are treated the same (two with pickup stitches and two with CO stitches, and then the bag will sit and look "right". Of course, alternately you could knit the bottom flat then pick up along all four sides... but that leaves you with extra ends to weave in.
Long story short, I have yet to see a pattern that called for PCO that I couldn't find another way of accomplishing the same thing, but it'll often be more work to not follow the pattern than it is to learn a new CO.