Yes, it fights childhood obesity. None of the rest is universally true. Let me go through them one by one to demonstrate.
1) leadership qualities Constant reminders of how I was at the bottom of the totem pole didn't develop leadership for me. You develop leadership by doing something you are good at, not bad at. My positive experiences only happened much later in life.
2) coping with adversity I got lots of practice with adversity. Particularly when my physical challenges made me a target for bullying. I never noticed that the experience helped me cope with adversity though.
3) how to win and lose gracefully If by luck I wound up on a winning team in PE, it was clear to all that I did not contribute to the victory. I got practice at losing, but never noticed that the other children learned to be particularly graceful at winning.
4) coordination (all sports take practice) Did you notice the bit about my having a medical problem which required therapy? Yes, physical activity builds coordination. But the way it was done in school did not build mine. I wound up fixing that as an adult.
5) fights childhood obesity This I grant. Though it was superfluous in my case. Everyone in my family is skinny until at least 30.
6) forces kids to be around other kids instead of in isolation Given the way it made me a target for bullying, isolation would have been better.
7) Experience working with a team from an early age For me it was so demoralizing that I never felt like I was really part of any team until I was in my 30s. And when I did, it was programming that got me there, not sports.
These will work for any child, not just me. Bullshit. I am a definite counterexample to your theory. As you would have known if you paid attention to what I said before.
I am strongly in favor of all children who are physically capable of it getting exercise. But competitive sports are NOT a good idea for everyone.