"Think of the children" as a phrase is meant to satirize the fallacious appeals of "moral panic" arguments in support of conservative social values.
Your idea that it also covers arguments for literally not killing children is odd. There's nothing necessarily fallacious about singling out children as a subset that it's especially important to avoid killing.
In this case half the civilians are children and they are being killed, so it's a reasonable thing to want to stop.
The implication of your use of the phrase here is that no one should consider children's wellbeing even when real harm is being done to them. I find that idea dystopian and inhumane.