NickB

You certainly have a point but, ultimately, I would probably agree with Misco60 that the only way to address this is through well-designed boarding processes. The problem about blaming both is that you end up arguing against human nature.
If somebody in group boarding 4 has been spending the last 20 minutes queuing, you might get them to stand back when groups 1-3 are called but they will still want to be the first to board when group 4 is called and you won't therefore get them to go back to their seat until group 4 is called. The only way to address this is to have a boarding process that, among other things, clearly separates out different groups in different locations/queues.