Thinking with a slightly clearer head, I can see how Katniss doesn't quite fit this trope. It get mentioned a bit, but there were other things to deal with in her story.

Thirteenth Child can be kind of hard to read, but part of that is because of how painfully right Wrede got the child's mindset. As the supposedly unlucky thirteenth child, Eff blames herself for everything. That gets old quickly, but it hits harder once you get that that's how kids actually think. When things go wrong, a child's response is to think that it's their fault, especially if they've been constantly told that they're the source of all evil, like Eff was. A lot of the plot of the book is her figuring out that she's not bad or even unlucky, and that she doesn't have to be afraid of herself.

For added bonus, the book has woolly mammoths and dragons. How much more awesome can it get?