I'd say winning is far more important in life than in sports. Dodgeball (which I think is great fun) was just an example of the things govt schools remove which relate to competition. Can't have anyone losing "self esteem" cause they just got beaned in the head with the giant red ball.
There's competition that encourages people to get better and to excel, and there's competition which is brainless, rewards people for stuff that is not easily improved, and makes people who are doing poorly into the center of attention. The Darwinian stuff can be constructive and destructive.
Competition is the greatest gift humanity and America have going for them, but dodgeball is as useful as having students guess what number the coach is thinking of.
Dodgeball strategy kind of mirrors socialism: you're constantly going after the better players on the other team while leaving the fat, slow kids alone for the end when the athletic kids have been eliminated.
It's kind of like the American tax system.