> orders of magnitude harder

They seem to be at about the same difficulty to me; it would be nice if you could elaborate.

If a private company fails over and over again it goes bankrupt and is dissolved. If a government department or organisation completely fails at their goal they’ll generally be given more money and resources. See many, many school districts in America, the CIA (failed to predict the fall of the USSR and 9/11), the Pentagon (Iraq and Afghanistan), the State Department (Let’s destroy Libya and Syria!)

Organisations very rarely reform or change. Usually they die and other successful ones take over their market niche. Where this doesn’t happen or happens very rarely things change very slowly.

Any competitor with the public school system has to compete with free at the point of access. Absent transferable budget per child local school systems have a huge advantage.