The more general issues are how well the modern world allocates talent and how much exposure you need to something you eventually will be very good at. 

My view is that people who are born into a reasonably good educational infrastructure get exposed repeatedly — albeit briefly — to lots of the activities which might intrigue them.  If the activity is going to click with them, it has the chance.  To borrow the initial example, most high schools and junior high schools have chess clubs and not just in the wealthiest countries.  Virtually everyone is put in touch with math, music, kite-flying, poetry, and so on at relatively young ages. 

The idea of taking an economics class in college, or picking up some economics literature, strikes most educated people at some point, even if they squash the notion like a bug.  If there is some other Paul Samuelson-quality-would-have-been who didn't become an economist, perhaps he preferred some other avocation even more.

Billions of people are not exposed to quality economics, math, music, etc., but those people also don't have the nutrition, the education, the infrastructure, or whatever, to excel at world class levels.  The infrastructure and the exposure come together and in that sense we keep on mining the pool of potential talent.  (Their only modal scenario to #1 for these individuals is an entirely different life altogether; mere additional exposure won't do it.) 

Ernest Bazanye is blogging from Uganda.

Some people get stuck in local genres, such as a brilliant Nigerian learning funk or rap, in his teen years, but not modern jazz and besides he can't find a Nigerian market for the latter in any case.  These "specialization corners" are less of a problem for math or economics, although the unification of those areas is fraying with time. 

Magnus Carlsen's father suggested that if he hadn't had an older sister, he might not have taken up the game at all.  Magnus was uninterested at ages four and five, but grew intrigued at age eight when he watched his father play chess with his older sister.  I read this anecdote as suggesting he would have been exposed again to the game, one way or another, probably in school.

Two scenarios militate against my thesis.  First, mistreated savants may not receive the necessary exposure to the activity.   I am very much a believer in the potential productivity of mistreated savants.  Still, I believe they often do best when not trying to be pure #1 in some commonly contested, measurable area but rather by filling unusual and hard to specify niches in a broader production process and benefiting from the division of labor to an especially high degree.

Second, a large number of children are placed on medication at early ages.  This may not eliminate their exposure to an activity in the literal sense, but it may stop them from responding to potential interests.

In sum, I believe that the odds that "the best (modal) chess player in the world" has never played chess is well under fifty percent but probably above ten percent.