The reason is that it IS a teamplay game, but there just isn't any objective... There's no reason to play as a team. If robbers had to rob a bank, then yes, people would work together to stop them, and the robbers would work together to rob it.
Without an objective, there's no reason to help teammates.
Yes, i think if teams had a "mission" to focus on then they wouldnt have the feeling of wanting to kill everything, well at least not always =P