“I’m a cop! So chill!”
You and I see this differently.
He probably knew this area, and had a good idea of what might happen to someone who is "the wrong color" involved in something like this.
Besides, if I stopped to help someone injured, I would say "I'm a paramedic/doctor/work in healthcare" to let people know I am helping the victim, that I know something about helping people who have been injured, and am not attempting to rob or scalp the poor person.
In his case, I would imagine it is his way of taking charge at the scene. I would have done the same. It dispenses with arguments that result from one person knowing nothing about the other. For all the father knew, the guy could have simply been a drunk bikie accountant.
Identifying himself does what they are trained to do. Set up a structure at the scene. I just don't see it as an arrogant move on the part of the guy.