She cares about going down in history and feeding her narcissistic ego. IMHO Hillary's whole life has been about getting ‘Gold Stars’. Some of us, when in elementary school, would get good work rewarded by receiving a gold star stuck onto our paper (this article about Sotomayer explains it, and also says something about this whole genre of people and what has motivated them through life: http://www.npr.org/2013/01/14/169363309/sotomayor-found-her-competitive-spirit-in-gold-stars ).
For people motivated in this way it's all about ‘winning the competition’ and ‘being special’, not about doing good and meaningful things that make the world a better place. Competition is a good thing, can push us all forward, and is a very positive force in the world. However, as part of becoming emotionally mature we make the transition in life that allows us to see the importance of doing whats’s good and right because it's good and right - and not because we will get credit and accolades. Not all people make this transition. Politics, academics, and the media are filled with people who never have. They never got past themselves, and perpetually need the gold star.
“Does she even care?”
In adding together the many stories I’ve heard about how Hillary treats people, I suspect she is a sociopath. A sociopath has no empathy for others and is concerned only about themselves. They enjoy the feeling that having power over others gives them. If that is the case, as President she might let lose what little control she has over her inner monster for the thrill it gives her.
There are numerous quotes over the years to the effect that Hell hath no fury like Hillary getting revenge. If it was your career at stake, I suspect you’d rather get hit with the ashtray she reportedly used to knock Bill unconscious.