Martin,
Just to gently correct you - "our children are never safe" is surely wrong. I guess that they are safe 99.999% of the time. Sometimes they might be vulnerable, but no dodgy people are around to take advantage of the situation. And at other times when they are totally safe, a dodgy person could be close but unable to do anything.
The obvious problem is when someone sees an opportunity in a vulnerable child. That is extremely rare, but when it happens the consequences can be horrendous.
Surely in reality my daughters are more likely to die in a car crash in the next week than get harmed by a stranger in the next 5 years. Just a guess - it really is unlikely. And I don't believe in fate or bad luck, so please no-one tell me that I will cause them to be in a car crash this week!