It's not an industry, it's a public service (I'm in France). Also they're saving lives.
If she walks away, that's one fewer ob/gyn in a region where they have almost none left in the private sector (the last one in town retired this year). Women and children will quite literally die and she knows it.

On the other hand that means she's more valuable and surely she should negotiate her salary from a position of strength, right?

But the set of people who become doctors and who negotiate with "would be too bad if something happened to women and children" is, as far as I know, empty.
If any exist, I don't think they'd last the twenty odd years of studying and training before they start making bank. Much simpler and faster to become a gangster.