Emergency room doctors
It's a mindset, not just a job.
You can pitch them as hard as you like about having them work to persuade their patients to give up smoking (after all, it saves lives in the long run), but I think you'll find that they're a lot more interested in stopping the bleeding.
We need emergency room doctors, no doubt. I just wonder if we have too many of them in your organization. If all we do is reward fast first aid in what people do at work, is it any wonder we don't have enough attention to the strategy and choices that would eliminate the need for all that running around in the first place?
It helps to know how prevalent the "emergency room" culture is before you start training your people on a new long-term strategy.