I don't know about you, but those are things I'd go to at most once a year so taking the train/driving downtown for those rare events wasn't a big deal for me growing up.
> free events for kids, concerts just for babies,
more details?
> parks
My friends and I used to play basketball, american football, and ultimate frisbee all the time growing up. Now I live downtown and the parks I walk past never have enough free space to play those kind of sports. Not to mention the walking parks and playgrounds in the suburbs are usually way bigger and less crowded.
> swimming pools
Suburbs have these too and one of my friends growing up even had their own backyard pool where we would play sharks and minnows, use the pool basketball hoop to play 21, or use the diving board. Playing the former 2 are much harder in a packed city pool then a suburban pool due to crowds, let alone a private backyard one.
> little league, soccer league, skate parks,
Had all these in the suburbs when i grew up and again, those require a lot of space which is in short supply in the city so there's almost always more available options to do these in the suburbs.