Big problems with this, even if we look past the silly complaining about "alarmists" etc.

You're making a common and simple mistake about moral theory; namely you're ignoring the issue that descriptive claims about morality are not the same as prescriptive claims about morality. The mere fact that morality functions as a method for people in society to cooperate with each other doesn't do anything to demonstrate that we are actually only obligated to cooperate with each other. What we're actually concerned with is what moral values people (or machines) should follow.

Your evasion of this issue is especially funny because of your claim to have the backing of "experts" on the subject - social psychologists? Sorry, the experts on the subject of morality are moral philosophers, and I can't think of any who would agree that the only thing of moral importance is just getting people to cooperate with each other. Don't we want more out of life than just to cooperate? What does "cooperate" even mean? Which moral transgressions do or don't count as violations of cooperation? What about animals and little children and people in comas and future generations and the legacies of the deceased - how do we cooperate with them? And people don't cooperate, so given that we're in a world without universal cooperation, what should we do? To what extent are we obliged to sacrifice our personal interests in the name of 'cooperation'? What about aesthetics? What about value theory? How is cooperation to even be measured and formalized? All big questions which need to be answered, and which can't be answered without addressing the work of actual moral philosophers (you know, the experts in the subject).

Now you don't like this, because it's a "rabbit hole", but morality isn't easy. (It is, after all, a hard problem.) That's the whole point. And rather than demonstrating that morality isn't a hard problem, you're saying that we can just lift a descriptive definition out of a dictionary, worship it like it's a categorical imperative and pretend like morality isn't a problem anymore.

Moreover, even if your avoidance of the distinction between prescriptive and descriptive morality were a good approach, you'd still be wrong. Human society is more complicated than evolutionary reciprocation and scenarios cut out of game theory textbooks. Morality is not merely a method of achieving cooperation, it's a source of power in society and a consequence of concrete social relations. Even if you want to restrict your domain to the descriptive side of morality, you will need to deal with tons of work in sociology and philosophy which shows how our moral views are influenced by our cultural and economic conditions and serve various roles in defining our roles in society.