That is among the many erroneous notions that props up statism. In today’s FEE piece, Max Borders slays it.

We had effective schools long before the state got involved. When it did so, by making schooling free and subject to government control, the incentives for cost control and efficiency were undermined. Over the span of time since government meddling began, the cost of education has risen greatly while it takes longer and longer to get young people to the point where they have a decent basic skill set — and many never do.

Nothing would do the US more good than a separation of school and state.