I live in a city similar to NYC (but not quite as dense) and IMO it's far better for kids than the suburbs.

I grew up in the suburbs and it was a miserable experience. If I wanted to go anywhere I had to ask an adult to drive me. There were no sidewalks. Nearest friend's house was a mile away, and my parents were understandably afraid of letting us go there alone. It was a 100% car-dependent suburb. Everything was so spread out. Nobody wanted to live on a main road with cars, so there were endless dead-ends and culs-de-sac so everybody can have their own little traffic-free neighborhood

One time I literally WALKED SIX MILES to the mall because I was just so bored. I literally spent about half a day just walking on streets with cars going 40+ miles per hour with no shoulder. What's worse is that I had to go behind my parents back to do it because who wants their kid walking next to F-150s going 40 miles an hour?

I thought things would get better once I could drive. Things improved a little bit, but it's hard to afford a car + insurance + gas at 17 years old. The car was a huge drain on my limited resources. I was so eager to get rid of it

Once I discovered the "rat cages" you're deriding, life became a whole lot better for me. I refuse to raise my kids in the suburbs. Kids deserve better than that.