Not really, the missing person could turn up pretty much anywhere. Even if it leads to a single success story of somebody being found, I think it would be worth doing.
There is significant opportunity cost in dropping everything to search for missing children. There is practically no opportunity cost in changing a 404 page.
not so sure about that. With 404 pages, a user was trying to do something, and it's pretty much guaranteed that it wasn't looking for pictures of stolen children.
A task-irrelevant interruption increases the likelihood that they give up or get thrown off task, and certainly delays task completion. A 404 page is an especially bad time to distract users because they're already in the weeds.
Were I wanting to use a site to help search for missing children, I'd probably just devote some of the ad units to it.
Additionally, it induces anxiety/sadness/etc in lots of people. Some can apparently just tune it out, but some are significantly emotionally affected by this kind of thing.
Problem is, the alerts are shown in Dutch and German on my french-speaking Swiss blog. I don't think my readers, when coming across a 404 while looking for something, will read "Verdwenen op 2-jarige leeftijd" and head straight to google translate to look up what it means.
What if it causes someone in, say, Massachusetts to memorize the face and name of a missing child in, say, California and doing so causes them to forget or concentrate less on some local missing child?
I don't think people have a "missing children" memory buffer like that. I might be wrong though. If anyone has links to articles on human memory segmentation it would probably be interesting.