It totally depends where you live.
Until recently we lived on a large estate, and the kids there had basically the same childhood (as far as running round outside, and no activities), as I had.
Some of them have good parents, and will probably do OK in school etc, whereas others were just totally left to their own devices, and went off the rails.
It's not the scheduling or not scheduling of activities that counts for much, it's the culture you live in, and whether respect for others and education are valued in your world, or not, and also whether your parents are coping, or, for whatever reason, they are not.
Those are the things that matter to children's development.
For the record, though morethan there are NO free activities in my LEA, other than one museum. No free swimming, dance, gymnastics for those on low, and very low, incomes.
I see what PureQuintessence is saying about children in Norway being more independent etc, but I have been to Norway, and I can see that there would be a world of difference being "independent and street smart" in Norway and independent and street smart in , say, Tottenham.
The "scrapes" that a British urban kid might get themselves into would likely be a Hell of a lot more serious than in Norway, so I just don't think it's comparable.