I don't think the system is that foreign to Americans. Soccer in this country has mimicked the rest of the world. An MLS team has their regular season and playoffs, a domestic cup, continental cup, and national teams.
College basketball isn't too far off. You have preseason tourneys, conference regular season, conference tournament, NCAA tournament (and the other postseason tourneys). Not to mention rivalry games that may include a trophy.
Pro sports in this country though is so heavily monopolized that the idea of outside competitions are non-starters.
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