Group are very fluid entities, and can be defined by pretty much any parameter, which make your statement a bit vague. But even without considering that, there are shortcomings in your theory.
On an individual point of view, being biased towards one group will reduce your own possibilities, it will also reduce the incentives for your group to adapt and better itself. To be fair, it has nothing do with your theory, but still is worth saying imo
Your proposition could also be interpreted has a prisoner dilemna, with each group as a player, not being biased is to cooperate and be biased is to defect. The rational decision for every group is to defect, but everyone would be better if everyone is cooperating. One solution is to have a higher authority impose cooperation, with non-discrimination laws for example.
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.
This sort of thinking seems bad:
This sort of thinking seems socially frowned upon, but accurate:
Similar points could be made by replacing a/b with [group of people]. I think it's terrible to say something like:
But to me, it doesn't seem wrong to say something like:
Credit and accountability seem like good things to me, and so I want to live in a world where people/groups receive credit for good qualities, and are held accountable for bad qualities.
I'm not sure though. I could see that there are unintended consequences of such a world. For example, such "score keeping" could lead to contentiousness. And perhaps it's just something that we as a society (to generalize) can't handle, and thus shouldn't keep score.