In adulthood, I've often thought back to that ludicrous ad. No child's fingerprints are getting checked unless some foul play is already suspected. The likelihood that the child would fall into police custody and get checked is already slim; fingerprints aren't going to help until that happens. We don't have campaigns to fingerprint children as a proactive precaution today (of which I'm aware). Clearly, that wasn't a major breakthrough in reuniting kidnapped children with their parents that endured.
I'm very cynical, but I've always thought that was a campaign to gather biometrics from the population using fear as a motivator. I don't necessarily think this is that, but I can't help wondering the perverse incentives of the FBI as I'm reminded of the ad.