being above the speed limit or below it can make the difference between killing the child and stopping in front of them.
No, it won't. That's hand-wavingly simplistic at best.
Driving at the speed limit won't magically make you dodge children like Neo with bullets. What it will do is reduce fatalities; beyond 30mph, the chances of causing a fatality with an impact increases sharply. It's bog all to do with stopping distances.
Driving at a speed commensurate with conditions will make a bigger difference than arbitrary limits. Driving past a school or between parallel-parked cars, the oft-posted 30mph is too fast. In poor visibility conditions, 30mph is too fast. On wet or icy roads, 30mph is too fast. On a clear, wide, deserted road at 3am, doing 40 in a 30 is unlikely to have you mowing down toddlers like skittles.
But many people don't have much common sense, so we have catch-all speed limits.
If you're driving around going "I'm alright Jack, I'm driving under the limit so I'm perfectly safe" without any consideration for conditions, well, I'm not the one who needs an awareness course.