When a child dies, or is dying, certain things happen, even to the shallowest and most facile of people.
First, they cease to be completely sane, at least in a normal sense. Coping skills break, perspectives change, a deeper level of emotion occurs, and fault lines are exposed.
Second, the state is exploited by others, who generally have no idea of what is going on. Most of the comments are "see, something terrible, which I can exploit for bathos" (well, they intend pathos, but you know how it is) or "see, people in the grip of soul wrenching grief, acting soul wrenched or out of complete control."
Third, they tend to find more contact with reality.
Which is why I was rather harsh in comments regarding the play On the Romance of a Dying Child.
In that play, two parents have a child they think is dying. In the play they have various emotions and discussions, appearing to come to embrace, in a shallow way, pity and self-absorbed views ("But now I have a dying child. That’s better than a big nose."), when they discover the child might not die. That leaves them with the closer: "(The doctor nods and exits. Pause. They look at each other. They look away. Pause.) What if he doesn't die? "
I only remark because the play is a good example of the typical use of the death of a child (real or fictional) as a way to exploit bathos for shallow, inauthentic and manipulative ways -- which you will see over and over again.
So, the play noted not because it is unusual, tripe, but because it is typical tripe, of a kind you should be aware you will be assaulted by continually, for the rest of your life, once a child dies.