Your “criteria” are so laden with question begging, it is obvious you framed them in such a way to lead to your conclusion.
You explain the paucity of black players in the NHL is the result of a relative lack of interest from blacks. I agree. Why do you not allow this same explanation for whites in basketball? Basketball is the predominant game in the black community. No other sport even comes remotely close. Sure, some whites like playing basketball at a young age. But they also choose between basketball, football, hockey, golf, tennis, soccer, swimming, lacrosse, baseball, drama, musical instruments, etc. You use absolute population numbers instead of proportionate numbers for interest in basketball. I wonder why. So no, the pool of basketball participants is not heavily skewed toward whites. Your assumption is incorrect.
Unbelievably wrong. The desire to excel in basketball is held almost universally in black culture. Being the best at basketball automatically puts you at the top of the food chain. It is not a game that you need to be coached to learn (I am talking individual skill, not team skill). There are very few rules. Put the ball in the hoop. Schools and facilities are almost immaterial. You need a hoop and a ball. Better family structure helps in basketball? Uh, no. Going to an expensive basketball camp does not make you a better player. All of those camps are just money making outfits. You get better by playing as much as possible. What do you do when you have a terrible family at home? You escape by going to the court to play basketball all day against kids who all want to be at the top of the food chain. The most popular kids are the ones that keep the best court all day.
Again, wrong. It has been said over and over (and it appears you acknowledge it), the only way for many people in the black community to escape where they come from is through basketball. Notorious B.I.G. said it best - “Either you’re slingin crack rock or you got a wicked jump shot.” Playing in the NBA is like becoming a doctor/lawyer/astronaut/president to kids in white communities. This is why almost every successful player in the NBA played basketball every single day for hours and hours while growing up. It is all they had. Go by courts in the hood if your city has not taken them down already. You will see them filled all day. Hell, around here you will see people playing basketball at any time of day. I mean it. I drive by at 4 am and there is a 5 on 5 game going on. This is anecdotal, but the white kids went home after basketball practice. The black kids went to the park and played 4 more hours. The idea that the motivation for whites to play in the NBA is as much as blacks is laughable.
Yes we can explain this pattern. It just does not fit into your confirmation bias. Nurturing heavily favors blacks. Whites have many more options and chose those instead of basketball, while blacks almost universally choose basketball, with football a distant second. You say whites choose other sports or to quit basketball because they see they are physically limited. I do not necessarily disagree that this is what is going through their heads. That does not mean they are physically limited, though. I submit it is a combination of whites misattributing their lack of skill due to less time played honing their skill as physical inferiority and the stereotype threat. See,
From Psychological Dynamics of Sport and Exercise - Diane L. Gill - Google Books
You clearly do not understand the cultural aspects of basketball. I cannot tell you what to do, but you should really think about coming up with another example to trot out every time this comes up.