Why is it wrong to look at the issue from a cost/benefit perspective? If an expenditure of resources isn't very effective at preventing child abuse, shouldn't those resources be deployed in a different way so we can prevent as much abuse as possible?

What's sad about that?

Benefits include things like "fewer children getting abused".

Costs include things like "children in formative years being told that a beat up child looks perfectly normal". (And, as hawkw mentioned, "opportunity cost of not being able to implement other strategies".)

"Think of the children!" is a potentially dangerous slippery slope argument that, on Hacker News, we often deride because of where it can go, where no logic and only emotions are thrown into the mix.

It just so happens that, in this case, you're actually affected by the argument being presented. Child abuse is an absolutely terrible thing, and we should work to stop it, and work to get those children that are being abused a way to be protected, and so on; but the question that others here are asking is "is this the right way to do it? Will this attempt do more harm than good?" and that's a good question to ask.

If 5 year olds everywhere are taught that black eyes are not potential signs for abuse, then Billy down the street might get missed, because mom didn't see the what the child said, when the kid, seeing the billboard, asked why "why is that kid hurt?"