Opportunity is obviously important. But then again New York, California, Texas, and Florida probably have more opportunity to find competition and mentors in the game then South Dakota, and yet the best player in the USA is not from New York or California or Florida or Texas.
And the idea that it is just "hand/eye coordination is a simplification and it is incorrect. The inner ability to excel at the game is more complex then that. Obviously Wayne Gretzky had hand/eye coordination, so does Tiger Woods, so does Roger Federer, but the chances are if Roger had of taken up Golf he would not have become Tiger Woods level, if Tiger had taken up Tennis he is probably not going to be the number 1 tennis player in the world for years straight, and if Wayne Gretzky took up golf or tennis instead of hockey he probably would not be world famous and hold world records in either sport.
Each sport takes a very specific type of mentality, a very specific type of brain make-up to excel at it. I took to pool very naturally and quickly became better then alot of people who had played alot more pool then me. In golf I have put in boat loads of practice and I still suck at the game. I was once a extremely good curler and became good very, very quickly at that game, and yet I have never been able to throw darts well despite playing the game quite abit. Every sport has its own unique aspects that each individuals brain has either a high or low capability in. Being good at one sport does not mean you will be good in another, and people who excel at sports such as the top pros normally focus on those sports because they take to them VERY quickly and realize they have abnormally high talents in them.
It is not just "hand/eye coordination", it is WAY more complex then that. The nuances that make a pro pool player have that potential within them is very specific to pool and simply not that generalized. Some peoples brains "just work" in certain games. Look at Chess, huge numbers of people try to reach the top of that game, very few players in the world show an abnormal talent for the game right from a young age and eventually become the top players in the world. Kasparov is not just the result of practice, there is something unique about guys like him. The top pool players are no different, they can do something that most people NEVER could.