In my experience this is very common in cities too. It's the suburbs that prevent it. I don't have kids yet, but in my (very urban) neighborhood it's extremely common to have kids out and about on their own. It's generally seen as being very safe.
When I talk to coworkers with kids in the suburbs they're much more worried about letting their kids run around without adults. To be fair, it makes some sense: cars are one of the biggest killers of kids, and they're a much bigger risk in the suburbs (where most streets are wide and fast) than the city.