Cooperation is certainly natural, too, for social species. But the compromise between cooperation and domination is tribalism, the way we end up in exclusive relationships with kith and kin (rather than with everyone under the sun). And those groups are organized internally along levels of dominance.

I'm not sure, then, we can count on our natural impulses to make us more moral. Morality seems to me as unnatural (idealistic) as anything could be.