The pilot has to keep the aircraft safe, but the mission is the whole reason that the aircraft is there in the first place. The pilot cannot be isolated from the mission, as you will lose a lot of the team effectiveness of working together as a crew. The crew has to be completely integrated on the task, otherwise the helicopter will not be in the right place to see the target and achieve the mission.
Yes the workload is high at times, and prioritisation is very important if and when there is a conflict between safety and mission effectiveness. That is why police pilots really need to have a shedload of experience before they are recruited into this role.