I think the very strong emphasis on sports in the US is multifaceted, but for children is particularly suited to strengthening the American ethos of group think, exclusion, and the law of the jungle.

These are the traits we reward in business, politics and the military, so it makes sense to use them in "games" to see who has the best characteristics to be the next sociopath in chief?

The best example of this is the game "dodge ball." Basically it is the closest to just saying, "You strong kids go beat up the weak kids for a while."

I'm coming from this as an athlete. I've played probably 20 competitive sports, and train 4-6 times a week still now in my late 50s. I just never found a team sport I really liked. It took me into my 20s to realize I like individual sports much better. Fortunately I didn't discover boxing as a kid, as I've got a lot of anger in me and I can't say as a teenager I wouldn't have done some bad things if I had trained at a bad gym.

As it was, I learned how to really hurt someone quickly at a time I was already in therapy. That is (I think) what also helped me to see things like organized sports in schools, as you so well describe, as a kind of "weed out the weaklings exercise" as much or more so than "let's get the kids some physical exercise."