I'd say that David Cameron's interjection added nothing and was pointless. It makes no real sense. On the other points, I almost see that using "as a parent" to lean into empathy is almost more limiting. It almost says to me that they can only feel that empathy because they are a parent.

But, in their defence, I would also argue that they are simply using this as their personal means of emphasis. What they are really saying is that I am a parent and the thought of this happening to my own child hurts like hell, rather than those who don't have children can't understand how heartbreaking it is.