Imagine a child dying from hanging in the "lynching game". When teachers are asked if they knew about they said yes, but there are no rules.
Even if it underestimates the effect of bullying (which I'm skeptical about), it certainly puts the school at much more risk for easy lawsuits.
But that's the whole point: when you actually do the experiment, all these horrible things that you imagine might happen don't actually happen.
No, not "no problems whatsoever" just "fewer problems than there are now." Which is in fact the case.
The problem is that people looked at the problems that existed before the rules were in place and applied an argument of the form: There is a problem. Something must be done about this problem. This is something. Therefore we must do this.
I hope I don't have to explain the flaw in this reasoning.
Nobody wants to see a kid hurt, but rules only get teeth when money is on the line.
"We watch the kids play, then we talk and they decide on the rules. They respect the rules better then".
Adult supervision at schools is pretty common, even in the deep South Pacific.