everyone would be better if everyone is cooperating

I agree with this view. And as I was not claiming that it would be good to be too much biased and always (or too often) defect. However, if there is a general tendency of how often / how likely do all the groups defect and cooperate, then one group who pledges to never ever defect no matter what, will see that the other groups will defect against it, solely because they know they will always win. The solution of the prisoner's dilemma requires the possibility, or at least the ability for you to defect, even if you don't choose it. Otherwise your opponent will always defect.