Might also have helped an ambulance get through if someone traffic kept moving.
I've been in a similar situation and most cars moved up the road a few hundred meters and then pulled over. And then ran around panicking. And I could have done with less people coming over and asking what they could do because in my head I was shitting myself and trying to remember my very limited first aid training.
I remember talking to someone that was an EMT a while back and she said people that aren't capable of helping need to stand clear and resist the urge to run up and be in the way, especially if other people are already with the person/people.
And you're right giving the situation space for ambulance, police, etc is the best move drivers could make unless, again, they're absolutely capable of helping.
As for my specific comment about stress etc, if I so much as see police lights in my rear view mirror my blood runs cold and I have a borderline panic attack. I'm not personally fit to respond to these kinds of situations. I can absolutely pull over somewhere and call 911 though.