Citation very much needed, because I believe this statement is wrong.

Child abductions by strangers have simply never been "rampant" at any time in America. A tiny number of cases ballooned to huge media prominence during the Reagan era, but the number of actual cases stayed very similar at less than a dozen a year, at least according to my memory from the time.

Nearly all child abductions are performed by relatives.

I welcome your refutation with sources.