I don't know much about the management of these things.
I'd just assume that it's American based organisations who are willing to buy up overseas players. I doubt many players care too much about what country they are representing. Also If we assume that certain regions are just naturally better maybe this would create an environment where overseas players would have a comparatively easier time dominating in American tournaments against American players over their own. Certainly isn't unheard of.
Are you talking football? Pirlo, Lampard, Drogba, Villa etc are old and have prooved everything in Europe. The US is an interesting country with a lot of money so they can still affort to pay them the same wages and like you said, they can play against other legends and meet them. The MLS is indeed less tiring and atractive but the players from Europe who go there are mostly old (30+) and don't feel like playing 2-3 games in week anymore but still get the same high wages. It is perfect for them. They are also being used as role models for the young American players so they can learn and make it to the USA nat team in the future. Logic. I have a Twitter account with almost 7k followers so i know what i'm talking about.