I feel like the number of people around her dying might have something to do with her own wishes. Not that Satsuki would wish harm purposefully, but for her to prevent deaths someone has to be at risk of dying. So something (a curse placed upon her, a curse she accidentally created, I'm throwing spaghetti at the wall) puts people's lives at risk so that she gets those opportunities.
I really hope I'm wrong and barking up the wrong tree.