As am I, Roman.
In fact you'll note in my text, I make specific reference to the seemingly arbitrary source of some of Craig Cochrane's numbers-- from which my work is derived. (Craig is known as Upper_Krust on these boards.)
Yet there's no doubt in my mind that whatever the origin of UK's numbers, his methodology is remarkably predictive of CR.
You may question whether that means that UK hit the bulls-eye, or whether he's simply proven out that "close enough" is good enough with respect to CR.
I tend to think it's closer to the latter, and I encourage you to look at the big picture.
The value shown for Hit Dice also includes a flat-rate constant for ability score increases, and a flat rate for feats: Regardless of the type of HD you use, you get 1 feat per 3 HD and +1 ability score per 4 HD. This is explicitly called out in the text, and it's why it doesn't scale the way you expect. This is your error.
Back out those fixed constants and here are the HD values:
d4 = .083
d6 = .1165
d8 = .15
d10 = .183
d12 = .2165
There is much rounding off in the text, but those figures are
directly derived from the average hit points per HD.
Thus they'll match the ratios you expect to see as HD increases.
I could go into greater detail but it's unnecessary to answer your question-- because it won't address your concerns regarding the arbitrariness of the numbers. You can still drill down to the cost per hit point and wonder why it is set where it's set, and let it annoy you no end.
I can't
make you comfortable with the arbitrariness. At some point you're going to have to get there on your own.
Don't lose sight of the big picture. Greater precision does not necessarily guarantee greater accuracy-- and the system that UK has deconstructed is reasonably accurate and reasonably predictive.