She won the battle because the Knights of the Vale fell into her lap because of who she is and because Littlefinger has some use for her. She's always had some political value, which is why she's been married twice and engaged to three others at various points. It wasn't any great character development that led to her winning the war. Had she played her cards right, she could have had the knights of the Vale from the beginning possibly without Littlefinger.
So she did it, but not in the style you'd prefer.
I'd love you to explain how she could have had the Vale Knights though.
Women in that world have their vaginas and family of birth. Dany is an exception because she has dragons, without those she has... wait for it, her vagina. Remember she was SOLD at the beginning too. Cercei talks constantly about how if she had a prick, she'd be running the show. But she has... wait for it, a vagina. Ironically brother Robb dies because, wait for it, he wanted verboten vagina.
As for the rest of your post, we'll see.
GRRM loves him some major protagonists dying, but he also loves him some redemption story.
So we'll find out. I think you're 100% wrong. LF's weakness is that he's always wanted some Tully vagina. And guess what Sansa has? A Tully/Stark vag.
Now that she's not a blushing maid anymore, she's fully aware of the power she wields, and where it lies.