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.
I'm sure if the president was physically incapable of wielding a knife, she would have someone on hand to do that for her.