That's fine if your explanation is as such, and I wouldn't argue against your opinion here. But as I point out here, there's nothing worth noting that's actually in the story so far that makes her an interesting character. All if her intrigue is in whatever people wish to project on to her as an otherwise uninteresting character.
And yes, I think we can say the same about Kratos, who really wasn't an interesting character at the outset. The game was interesting because of its gameplay and mechanics more than driven by the character's story. I'd persoanlly say Kratos as a character only really started getting interesting in the 3rd game, when he recognizes the actions of his past. IMO it was a strong setup for the current God of War series, and a much wiser, older Kratos.
I wouldn't point at any of the earlier God of War games as being strong for their story or characterization. It was a mindless action-blockbuster. The story was really just an excuse to kill a bunch of Gods.