1. Kids are more spread out. A suburban neighborhood is huge and fewer people are having kids. The people that have kids will have fewer of them. For kids to coagulate together for playtime, you need higher density.
2. American roads are fucking deadly. Bigger cars at faster speeds with ever less attentive drivers. Cars are by far the number one killer of children and American voters do fuck all to fix it. If we banned all cars, I'd probably let my 2 year old mostly wander around by himself until dinner.
3. Dual working parents plus shitty workplace policies mean there are just fewer eyes out there. Even in the old days, "Free Range" didn't mean Lord of the Flies. It meant the kids roamed around but there was always an adult nearby, even if not in any official capacity.
A combination of 1, 2, and 3 makes for American parents structuring a kids' life around schleping them to various scheduled events and places. Even when a kid gets older, they've never developed the habits to do it for themselves.