Doctors regularly have people's lives in their hands and if they make a significant mistake, they are liable. Not that the current state of medical malpractice law is exactly the gold standard, but that's an example of another approach to a similar situation. I do hear that some folks avoid the profession because of that, but I don't think that it's the case that "no reasonable person" wants to work in healthcare.

I don't think most reasonable people want police to be personally liable for every single thing they do, but neither do they want them to have broad and complete immunity from the law. The answer is somewhere in the middle, where police are protected in certain situations, but do still need to think about the consequences of their actions.