Yes, this. In the USA, children don't play pool. There are zero elite players, that did not play, as a child. It's that simple.
I think this is quite important, in Europe we don't have the same stigma around alcohol as you guys do in the US.
Of course all pool halls sell alcohol, but they simply don't serve children (the definition of which varies country to country, but in most places will be 16-18).
In the US I get the impression its much harder to go into a pool hall and play if you're under 21, whereas in Europe you just go in, play and aren't allowed to buy alcohol.
Quite often there are rules for the evening too, for example no children after 7pm, or sometimes no unaccompanied children, but it still means there are plenty of opportunities to play (assuming there is a venue nearby, which of course isn't always the case, even in the cities).