So I'm picturing your scenario of 25 kids sitting in an open field surrounded by 5 teachers. You are leaving out the building, the busses, the gas for the busses, electricity, natural gas, insurance for sport teams, uniforms for sport teams, stipends to pay coaches, computers, supplies, desks, chairs, principals, assistant principals, librarians, computer techs, cafeteria workers....... But those expenses aren't exclusive to the public school system. And besides, buildings, busses, uniforms, desks, chairs, etc are re-used from one year to the next.
Oh, books, forgot books. Now there's a racket for you. Our English book costs $87 to replace; the math $74. Someone is making some serious bank on selling books.