There would be literally hundreds of children playing daily in that park when the weather was nice, and usually a smaller number when it wasn’t as nice, but still hardly ever zero during reasonable “kids playing outside hours”.
Ages were between kids that could barely walk there with parents or nannies all the way to young teens.
I’m sure many other cities are not like this, but in neighborhoods where people with children in NYC actually live (like the UES) there are plenty of parks and people to fill them.
Quite frankly it’s a miracle that the school district works at all. Having experienced it, school choice does not scale to a million plus kids.
Mine has a community sports league for just about anything you can think of. Swimming, soccer, baseball, lacrosse, touch football, cross country, etc...
There are four different community swimming pools, miles and miles of hiking trails, and sidewalks everywhere for bikes and dog walking. Courts for tennis and basketball. There are kids everywhere. It isn't unusual for the doorbell to ring with a kid wanting to know if your kid can come out to play. One neighbor kid used to ring our bell to ask if he could go in our backyard to play with our dog. On days like hallowe'en, people block the roads off and kids run wild.
There are elementary schools and middle schools spread throughout the neighborhood. Kids can walk or bike to school, although lots of busy parents still drive their kids.
This is not unusual in Manhattan. Pick any apartment and walk five minutes in every direction. You'll find a playground.
In the winter we take the subway 20 minutes to a large indoor complex with better equipment and hundreds of other children. They are not quiet!
Of all the places we go, his favorite is the subway, where he gets to say Hi! and Bye! to lots of people.
I dread the loneliness of the burbs.