"The main issue I see is that team sports are based on mini-nationalism; my team versus your team..."
I just see this as the nature of competition itself, especially in sports - since the purpose of competition is to defeat your opponents and become the champion.
There is some negativity and a lot of adversarial behavior in sports today, but that has a lot to do with horrible fans than the actual competition itself. The players frequently feed into it, but it's not as bad as most people believe it is. I don't go so far as saying that it similarly represents nationalism of the state. Even if it did, there's nothing coercive or harmful about liking your favorite team or disliking another team.
That is, in itself, an issue. Competition is necessary for survival in the wild, building it into culture is done because of how much it props up the ideas of statism, nationalism, corporatism, and all of these other sociopathic issues we are dealing with as a species. Conditioning is always going to have much wider-reaching ripples than the immediate physical activity that's being looked at.
Except for the fights, riots, and other violence that often happen around large sporting events.