It's not really necessary to compare the numbers of the NBA and NFL players. NBA players play 82 game long seasons (well prob not this year) on 12 man teams where injury prevention is much more important than standing vertical jump. The point is not that NFL or NBA players are great athletes in so far as their vertical jump or sprint speed but that the NFL and NBA take attract a large percentage of talented youth who could otherwise go on to find success in athletics or weightlifting. This is indisputable. Reggie Bush was a mid 10 100m runner, Nate Robinson was a talented 110 hurdler, Javhid Best ran mid 20.x in the 200m, all in high school. I ran against some of these guys. The showed promise, but I guarantee none of them could outperform their high school PR's today. That's because the NFL and the NBA don't make you better at running 100m or 200m or hurdling. They are great athletes because they displayed impressive times at a young age and with limited training. It's impossible to say which of them would have gone on to world-class performance because you really never know... In athletics some people peak at 18 some people at 36.
However, it's not a reach by any stretch to say that a great many athletes who are either in the NFL or NBA (or attempting to make pro-careers out of basketball or american football) could have gone on to great careers in athletics. The US has an incredible amount of ethnic diversity, areas with great weather, lots of money for sports, and well over 300 million people. If the US had the type of cultural focus on athletics that Caribbean countries have you wouldn't see a country with 2.8 million people (Jamaica) out-representing the US in the 100m and matching in the 200m.
all true. still doesn't answer the question of why we suck at olympic lifting, although the lack of cultural emphasis is certainly part of it.
I think the reason's the underwhelming performance in olympic lifting are actually less about overall culture of sport and instead come down to two things: the US olympic weightlifting program, and the parents of american kids. Olympic lifting is essentially a fringe sport for the entire world. As I explained above, most of America's best potential athletes focus on American football or basketball. Most of Jamaica's best athletes focus on athletics. However, countries which succeed in olympic lifting do not have that same level of cultural focus on weightlifting. In Bulgaria, Greece, and Iran (all successful at producing weightlifters) most of the best potential athletes focus on soccer. You could make the argument that the entire world is under performing in weightlifting in comparison to athletics and team sports.
The fact is weightlifting will always be a fringe sport because of it's technical difficulty. Children can race or play football or soccer in the schoolyard... But you won't find kid's doing clean and jerk and drop snatches at recess. To perform well in weightlifting children have to begin at a young age with excellent coaching and resources. The best comparison to olympic weightlifting is gymnastics. In the US the sport system usually involves: schoolyard play as a young child, competitive local competition and minor training as a teenager, and more advanced training as a college athlete. This model does a good job in sports like american football and basketball where the need to develop skills within a team is important and the simple physical development required prevents most athletes from being able to become elite professionals until they reach an older age. The model also does not hinder performance in athletics that much because athletics require less time devoted to developing technical prowess and requires a lot of recovery (ie 100m sprinters cannot and should not train 8 hrs a day like gymnasts). However, this model completely fails when it comes to developing athletes to perform well in individual highly technical sports such as tennis, gymnastics, etc. Here, the American emphasis on school and college sports simply wastes years for the athlete when they could be focusing 100% on their individual skills for their sport.
The best way to produce great athletes in a sport like tennis, gymnastics, or weightlifting is to take very young children who show glimpses of athletic potential (or have parents that found success in sport) and have them to train many hours a day every day in their sport. The sheer technical difficulty of these sports requires that the children have constant coaching rather than hone their skills against each other. If they train without coaching it will in fact be detrimental as they will develop poor technical skills which will effect them negatively at an older age. This is why you can find great soccer players perfecting their game in the streets but you will never find young tennis players with one-handed backhands unless they have coaching. Obviously, the inorganic development required to succeed in these sports means that, given the choice, most children will not voluntarily decide to attempt to be elite gymnasts or weightlifters. Thus, in a democracy where the state cannot select children to train at specific sports, given the choice, almost all children will choose to play schoolyard team sports like basketball, soccer or football with their friends.
Why then is the US able to produce competitive gymnasts but not weightlifters? Well, in a democracy the State will not force the children into the rigorous training... but that doesn't mean the parents won't. And in the US there are a great many gyms where parents devote long hours to encouraging (ie forcing) their child to perform the necessary training to become a great gymnasts. That's why most elite American Athletes in these sports have stories about the role of their parents in their development. For example the Williams Sisters were pushed by their father, Andre Agassi by his father, Shannon Miller's (arguably greatest american female gymnast) mother took her to Russia at age nine to train in gymnastics, etc. In contrast you don't hear stories about Michael Jordans parents pushing him to be great at basketball.
So until you have either 1) The govt placing value on american weightlifting and encouraging/forcing young children to do it or 2) significant number of American parents decide they really want a weightlifting champion for a child, the US will continue to under perform other countries.
Point #1 is not going to happen for obvious reasons. Point #2 is also unlikely because while parents can justify forcing their children into tennis or gymnastics because of the possibility of a college scholarship (a joke, because most kids who earn tennis scholarships had parents who sunk in 10x the cost of their education on expensive tennis training) or possibly money when the child becomes successful... there are no scholarships for weightlifting and almost no money in it's success.
However, that doesn't mean their still won't be a few crazy parents who want a kid with a 600lb clean and jerk. Maybe the child of someone from Brozknows will end up the next great weightlifter... We will have to wait and see.