Maybe that's true in small, peaceful countries like Denmark, but in the US children "excersising some independence" would likely be kidnapped, raped or killed.
The probability that any given child will be kidnapped or otherwise threatened by a stranger is minuscule compared to the chance that they will be abused, kidnapped, or killed by a family member.
That's sort of the point about low probability events though, it doesn't affect the average but it has a significant impact on the individual.
How much does it depend on where in the US you are?