Even before helicopter parenting was a thing in America (and this continues to hold today), the vast vast vast majority of abductions happen by a relative of the child. Abductions are already very rare, but of those that happen only 3.1% are by a stranger[1].

[1] https://www.seeker.com/child-abductions-by-strangers-very-ra...

Aren't the extreme measures a recent thing, like the last 10 or 20 years?

I don't remember being Molly cuddled like today's kids and I'm in my late 30s (UK).