My only problem with this theory is that the story was always meant to show that Kratos was not redeemable; at least, not truly (which is why I wasn't fond og GoW III's ending). In Jaffe's original idea for the series (which he revelaed in an interview), Kraots was basically going to become the "God-Killer," and was going to proceed on a rampage through the rest of the Mythologies of the world, starting with Norse mythology, if I remember correctly. Basically, he would have become so far removed from his original "Trying to be redeemed" self, but the concept of a truly evil character, one who gives no thought to his actions, and only does them because he deems it necessary to make himself feel better, would have, in a way, worked. It would have shown, instead, that one evil is less than another evil, and that the lesser of those two is the best choice.
Or it would have been a muderous muscley man running around comitting deicide. Either, really.
Now, for GoW II, Barlog had a different idea. In Barlog's God of War, at the end of the series, Kratos was to become Death personified; he was to become the Grim Reaper, with his Blades becoming sickles chained to his arms. Essentially, it would be (from what I can tell), both a reward and punishment: He has achieved a feat so great that reality itself made him into an absolute being (Death personified, something no-one, excluding him, can escape), but it is also a punishment, as he is now forever bound to this duty of being the Reaper, and can never find peace with himself. He would be bound to the chaotic nature that drove him to this in the first place, but would be undefeatable.
Neither ending inspires much in the way of empathy from the players, and the one from GoW III, well, "Critical Miss" did a comic about it which stated it better that I ever could.
No matter what, though, I still think the idea works; Kratos, from what I can tell, wasn't supposed to be redeemable. He was supposed to be on the right path in game 1, but by game 2, his insanity was supposed to be taking over; basically, because the gods didn't take away the memories. In GoW II, Kratos is to have snapped completely, not because he didn't get what he wanted, but because he no longer had, as you said, a goal. It was the goal that kept him sane, and without it, he fell to madness.
Simply put, in GoW 1 we control a sane, extraordinarily desperate, and unstable man. After that, we control a psychopath, one who has fallen into the depths of a broken psyche, and one who can never escape.
At least, that's how I see it.
I did enjoy the video though, else I wouldn't have written such a long response to it.