As someone who never played group sports I don't get this. I can see it developing leadership skills if you're the captain, but how does it develop leadership skills for the average player?
Anecdotal but...
My son was an average player and eventually 5 kids left our team for travel teams. It was going to a rebuilding year and we were going to lose, a lot. My son had been playing 3 years and the coach was the same so he knew the plays and on the field he would be instructing the kids to cut, slide, etc. really out of desperation more than anything. But the new kids looked up to him and eventually he was the go to kid that the other kids trusted and they would pass to him, where in the past the pass went to the "best kids" and he eventually became the "best kid". That is why club level is important. It gives the "average kid" the opportunity to be a leader at his level. He also loves it so much he volunteers with the little kids levels, scooping and catching. That has helped him be a "leader" and it teaches him patient, etc.
Also, I think it has taught my son how to lose gracefully. It took years to learn that but when 5 players leave your team it takes time to play like a team. It is something he has come to understand and can take a lose in stride.
I think the best position to learn leadership skills is the goalie position. If you are a good goalie everybody listens to you. You have to read the defense, tell players where to go and when to slide, etc. you also are fearless. Have you ever been hit with a lacrosse ball?