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.
This has never been significantly true, and becomes less true every year.
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.
By that thinking, looking at the data, you should prevent kids from seeing their family… Understand the nonsense? But nonsense gets often commonsensical when everyone in your circle believes it. Going outside has more benefits than risks. Like biking, yes you are at risk of accident, but in the average you’ll be fitter and live longer.
The US has much better access to mental health care than any European country. Not to mention everyone who lives in a walkable city there lives in a state where healthcare access is good.