I'm puzzled why people think putting a bunch of unsocialized children in a pile will turn them into civilized adults.

The impression I have of public schools (at least the good ones) is that younger children are pretty closely supervised, and that much of what elementary teachers do all day is say "No Johnny, that wasn't nice, apologize to Suzy", or "Suzy, you need to share the scissors with Tommy."

The children are practicing social skills with each other, but it's a structured environment with adult supervision, and with adults who are specifically trained and tasked to help improve the children's social skills and emotional maturity.

An elementary school classroom that feels like Lord of the Flies, socially, is a very badly run classroom.