I partly agree, but isn't that more of an issue about children being barbarians than about school being a barbaric institution?
As you say, adults only have control over superficial parts of these dynamics. I'm dubious that they can exercise more control without extensive restrictions on the youths freedoms and in turn their development. So these problems just seem inevitable wherever groups of children or teenagers meet.
People describing their school lives in modern Western countries will tell you completely different stories. From almost idyllic to hells of abuse (even sexual) and bullying that made them consider suicide before the age of twelve.
If we judge schools by the average, they are much better than the Spartan agoge, but if we judge them by the worst ones, I am not sure if it is still the case.