Well that's my point, the parents thinks its a dude in a white van to be scared off.
But the numbers say its the actual white van going too fast on a four lane road (speed limit 45mph) next to the park. This isn't that much of a problem in older European cities.
The city I grew up in was levelled by Nazis during WW2 and rebuilt to be car-centric.
The OP said that everyone is walled off by cars so they have a mindset of controlling their children, lest they get run over. You're saying that they're actually afraid of kidnappers etc., while they should be of cars. To me these points are contradictory.
In any case do you think removing cars will solve the problem? My guess is that no, because this mindset appeared decades after cars took over, and these things are actually not related.
If the cars caused the mindset then the mindset would necessarily be delayed by two generations because mindset and worldview changes require new humans.
https://reason.com/2014/08/19/august-2014-reason-rupe-nation...
Americans are split regarding whether there should be a law requiring 12-year-olds be supervised when playing in a park - no cars there.
As an European, to me this is absurd. At twelve I had a bus card and the privilege to go wherever, as long as I respected curfew.