New York has a walking and transit culture similar to Tokyo. Yet most New Yorkers would not feel comfortable sending a six year old out alone. I don't think walking and transit use is alone responsible for the difference.
Even in the rough and tumble NY of 40 years ago, parents allowed kids to roam freely up until the tragic disappearance of Etan Patz in '79. [1]
Seems like that event and the subsequent media fearmongering is what really spurred the cultural shift towards helicopter parenting and a reduction in youthful independence in the US.
It does come down to the fearmongering I think. People are really poor at judging risks and when more and more risks are made present to their awareness they make poorer and poorer decisions.
Native New Yorker here. Growing up in the 80's and 90's (when crime was at it's peak), it was common among everyone I grew up with to ride the subway/bus alone and generally explore the neighborhood alone/with friends. I remember my mother being slightly apprehensive when I started commuting to school alone in 4th grade, but it wasn't a major issue.
As many have pointed out, the culture has simply changed. Crime is way down, but ironically people are more afraid to let their children travel unsupervised than when I was a kid.
As a side note, I did get lost on the train once (while in the care of a relative. She got off the train and forgot to take me with her.) I was asleep and woke up at a stop I didn't recognize. While I remember being a little apprehensive, I simply walked over to the woman in the token booth, explained I was lost and had gotten separated from my aunt. She let me inside the booth and called my mom, who came and picked me up. All in all, it wasn't a huge affair. I think if that happened today police and CPS will probably turn it into a major incident of possible child neglect.
Yes? Of course it's a wild generalization. And by 'children' I mean young children, like we were talking about; and I'd have to qualify 'New York' somewhat if we had were going to quibble about it.