When free market doesn't work, free market advocates have their solution : there wasn't enough free market, so we need MORE free market.
People like you think the government should solve a problem that they themselves created.
In theory, but in practice there are many markets where that simply doesn't work, mostly due to natural monopolies, such as any type of infrastructure, healthcare or education, where competition is impractical or impossible, equal access for everyone is extremely important, and costs are high.
Still, nothing really stops competing methods and prices for teaching to competing levels.