McGrath, several Latin American countries have good players, some of whom are good enough to play in the USA major leagues and do play there. They have leagues in their own countries, but smaller populations, other major interests such as soccer football and lack of the millions-billions of dollars involved in American baseball, would prevent them from competing on the American level.
Baseball is big in Japan, and a few players have made it to the American major leagues.

The Cuban situation is amusing; the players "defect." Every Cuban, in fact, who defects and makes it ashore can stay in the USA; this has made Florida into a major Latin American "country."

Mentioning the obvious, many of the top Latin American soccer players work in European leagues and only play for their country in competitions outside of league play. The same with ice hockey; top players come to the American leagues to get big money, sometimes in the millions, but play for their country in the Olympics, etc.

Forgive me the remark about "other team sports," soccer football is very popular in American schools and in not too many years, I think professional soccer will be as big in North America as it is elsewhere.

All of which comes down to the fact that big sport is big business. In the first days of baseball, before the farm systems, many teams were local, and rooting for the "home team" meant something. It is, I think, a big joke today. I watch professional sports sometimes (tem minutes of Monday Night Football on TV is usually a prelude to two hours of napping in the easy chair) just to marvel at the ability of top players, but I can't get serious about them.