You do what you have to do to take charge of a scene like that. I've also had the misfortune of dealing with serious and even life-threatening injuries. I guess I'm lucky because my brain does not shut down, but rather goes into overdrive. So I naturally end up taking charge whether I want to or not.
You're absolutely right about crowd mentality, too. You have to expect that most of the bystanders will be almost useless and order them about. I never told them to do jumping-jacks, but I do give specific instructions to specific people and that works a lot better.
But I know what you mean about seeing horrible things. I try not to think about Grandma lying in a pool of blood, even though I saved her. I hope I never see another compound fracture again.