The 13 colonies broke away long before the rise of organized, codified team sports. OTOH, the Anglo influence and ties to Britain were always strong, particularly in the late 19th century. You could call the USA a "cultural" colony in some ways, I suppose.
The majority of soccer fans in the USA according to polls are not in favor of this system. It is the system we unfortunately have because of the cartel that is MLS and its collusion with the USSF. You're starting to see better football atmosphere at fourth tier clubs like Detroit City FC than you do at many MLS clubs. The reason is Detroit City is a real club built up organically and connected to the community while Houston or Dallas (or insert any franchise with dull atmosphere) are plastic inauthentic franchises.
Wow man, that's really insulting to fans of those teams. I bet you wouldn't say that in their BigSoccer subforums.
Mostly it's the sport, not the system. If there was something intrinsically inauthentic with the American franchise system we would not have the four major leagues in the U.S. It's not hard to find NFL fans who rarely if ever actually go to games, but view their team as a legit part of their lives. Conversely, jumping around and singing at a minor league soccer game for 90 minutes does not indicate a more authentic dedication to following a team, although certainly it can be a great core of interest to build on.