It is so sad that there are children who are not allowed to play freely. In western society many children (too many) are denied the opportunity to discover the joy of just playing. In schools recesses are being cut or cancelled then parents/caregivers are picking up the children from the school sidewalks and often driving them to organized sporting teams. One could argue that competing on those team sports is playing, yes, it is, but it is directed by adults and rules are enforced by adults. What are the kids learning? That adults make the rules and that they (the children) can follow directions. While many good things are learned and experienced through organized sports, that shouldn't be the only exposure to play that a child should have.
When children organize their own games they learn co-operation, negotiation, compromise, leadership skills, organizational skills and having fun for the sake of having fun without an adult telling them what to do, or hovering. Hmmm sounds like the same skills that organized sports boast, yet for less money and travel time!
I can't remember which group did this experiment but it was fascinating. They took a group of kids who were members of a organized basketball team and had them organize themselves on the official court inside the gym and then outside on the asphalt play area. Inside, the leader was the team captain and the boys played their usual spots. Outside, they organized themselves differently. The ones who took charge were the ones who were quiet followers. This shows that if a child has only one type of play activity there are children who would lose out on opportunities that could develop leadership associated skills. Sooooo, let children organize themselves, let them make mistakes. It isn't like they're going to ruin their chances to be a successful athlete if they don't practice, practice, practice in only official situations.