Can no one learn how to fix a fence or do something constructive? There has to be more to life than sport. Yes, it's an escape but only a very temporary one for most people. A true escape takes a bit more effort and commitment than playing the game you like to play.
From my experience, you start with what draws the target audience and you grow from there. It just happens to be the case that basketball is a good draw for a lot of kids in poor communities. But so is bicycle riding, tennis, baseball, football and other activities (like swimming at a pool!!!). But getting kids' time and attention is, I agree, just a beginning. From that other life lessons and habits can be encouraged through leadership, including the value of education and civic responsibility. But a lot of kids living in poverty have trouble seeing a way out of the circumstances they hear adults talking about so they end up wasting away thinking there is no way.
Oddly enough, of the many folks I've talked to about finding success in life though raised in poverty, quite a few have said when they were growing up they didn't know they were poor. They didn't feel held back by poverty because they never realized they were living in poverty. In each instance of this the parents were responsible for not teaching their kids that they lived in poverty. I found this a novel idea and it really resonated with me. I recall instances of watching our dogs play under the house when I was laying in bed at night looking through cracks in the floorboards. It never occurred to me that we were poor. I knew a lot of kids we went to school with seemed rich by comparison, but otherwise I thought most everyone else had big cracks in their floorboards just like we did. I thought we were normal!