Somebody is going to be appointed new CEO, and I think it's hard to deny that "if you produce too many bad health outcomes that reduces your own life expectancy" isn't a powerful motivator, no matter what the rest of the system rewards.

In the unlikely event that they appointed a CEO who felt sufficiently at-risk to issue orders to improve health outcomes at the expense of profit, how much effect would those orders have? Most likely the people below him would just ignore that CEO, find ways to rationalise that he didn't mean what he was saying. If necessary the board would go around the CEO and talk to the layer below him directly.