I think it would work equally well if the president had two aides and had to order one to butcher the other, in front of her eyes, in order to launch a nuclear strike.

Regardless of the exact details, I think the point of this thought experiment is that for a head of state, the decision to launch a massive attack that will cause hundreds of thousands of casualties can feel a little abstract. "Bombing a city" can seem abstract, even if the president understands this means killing children. Understanding is quite different from feeling. However, if the act of ordering a bombing raid on a city involved physically murdering a child, it would definitely feel more immediate and less abstract.

Your point stands, of course. But the part about removing the abstractness of the act seems relevant when ordering people killed.