As a warrior king, David depended on the ability of his commanders to channel violence, who were rewarded for that capacity. But would that control be perfect? What if David learned that one among them was beating his wife?
Would David have felt responsible for creating the circumstances of her suffering? What if that had been her lot for years?
Remember that God warned the Israelites against monarchy. This is not only because it places barriers between the people and God. It is because it creates pressures on kings that they do not have the wisdom to manage.
Now go back and read 2 Samuel 11 and ask if this would not be the story that Uriah would have begged David to tell so that he might die in honor on the battlefield. And that Nathan’s intervention was simply a charade for restoring David’s legitimacy?