I see your point, but once you get beyond that this arguement crashes.
Professional soccer throughout most of the world actually displays more chacteristics of capitalism than American sports leagues do. For one thing, there is no salary cap, revenue sharing, or luxury tax imposed on teams in the vast majority of soccer leagues, whereas these all exist in one form or another in the NFL, NBA, MLB, and NHL.
In the NFL, the most popular league in the US by far, the most successful teams are punished the following season by being given the most difficult schedules, and the weakest teams are rewarded by getting weak schedules; parity. This does not happen in soccer leagues throughout the world. In fact, in most leagues (except for the US) the weakest teams are punished via relegation to a lower league, while the best teams in the lower leagues are rewarded via promotion to the upper league. Contrast this to every single league in the US where the biggest losers get the first choice of new young talent in the draft.
If anything, it is our sports in the US that follow a socialist model, while soccer leagues throughout the world follow a capitalist model.
MLS has a salary cap chief