I am occasionally guilty of moving on to the next group ahead of the bulk of the team. But I do that because I otherwise have to either hold back in the use of my powers, look around for a non-dead critter, or leave everyone else looking for a non-dead critter. That all depends on the team and the critters, of course.
I might even run to the end room out of habit, but then I ask if I should ATT, finish it, or wait and then will comply.
I do recall once on live joining a Synapse team with a friend of mine and a few other folks we didn't know but they seemed to know each other. We wanted to speed at least through certain parts, Like Bertha. There are lots of kill all missions in Synapse already. They insisted that every single thing needed to be killed. We asked if we could meet some accommodation in the middle; they were not interested. So we quit, restarted as a duo, and finished before them. We played our way, they played theirs.