Think about two of the more important types of international competition out there for team sports. Use the analogy from Football (soccer for us US types) of the UEFA Champions League, and the World Cup.
Now, consider the big 3 team sports in the US (Football, Basketball, Baseball)
What foreign leagues have champions good enough to compete in a Champions League type competition in...
Football? Aside from major rules changes between the leagues, I don't think anyone would want to see the Grey Cup winners against the Super Bowl champs.
Baseball? The Japanese League is likely the best league outside the US out there, and they're basically AAA level (with some Major League caliber players, but not all of them)
Basketball? This is the most interesting of them. With the development of the sport in Europe and South America, I can forsee a day where this becomes a viable idea. Just not yet.
Likewise, a World Cup type setting, wtih the best players from a nation?
Football? Yeaaaah, right.
Baseball? This is a bit more interesting. Of course there have been steps in this direction in recent years.
Basketball? Also, a bit interesting. The US success in FIBA and Olympic competition has been problematic. I don't know that the US really takes it that seriously, but it can work.
Yet, even when you consider the last two, they really don't get a great deal of attention in the US. A fairly standard Free Agent signing in football or baseball will likely get much more attention than the FIBA semi-finals, assuming they happen the same day.