According to Harry Potter Wiki, there are 48 National Quidditch teams. This seems like an extraordinarily high number considering the low number of known schools of Wizardry that include Quidditch in their curriculum. Are we to believe the 432 players, 7 per team plus 2 reserve players (unless the big leagues have more reserves), all came from the 3 Magic institutions mentioned in the Goblet of Fire?
From this answer, we know that the total population of wizards is around 300K to 1 million globally. As you mentioned, the team size is 9, times 48, so less than 500. That seems perfectly reasonable. Just remember that there are more schools than just the 3 mentioned, those are merely the schools for Europe.
The Harry Potter Wikia mentions that there are more schools in existance than the three in the increasingly-innaccurately-named Triwizard Tournament. We know the American one is the Salem Witches' Institute... which indicates that there is also a _____ Wizard's School Somewhere in America (as magic users are, evidently, as sexist as us Muggles). The Wikia states there is a mention of a South American school as well, possibly in Brazil, but I don't recall that myself. Assumably there are one or more in Asia, Africa, and at least one Down Under (Edit: NOPE).
But you also have to realize you also slightly contridicted yourself - The 3 Magic institutions mentioned in Goblet of Fire are Schools, and there are 48 National Teams. That's like being confused why there are so few members of the New England Patriots are from the University of Miami. It's comparing Apple to the US Government.
EDIT: JKR has now released the names of the other Schools (again, not nations). They are the Uagadou School of Magic (Africa), Mahoutokoro School of Magic (Japan), Koldovstoretz (Russia), Ilvermorny (North America), Castelobruxo (South America). She further indicated that Durmstrang Institute is in either Sweden or Norway (maybe on the border?) and services Northern & Western Europe whilst the Beauxbatons Academy covers Eastern Europe (everything east of the Western border of Belgium/Luxembourg/the Netherlands).