You raise some good point, but I disagree with your main one.
The biggest failure in education today is not the government and the teachers' unions. The biggest failure in education today is that the very notion of "public education" is completely incompatible with the basic principles that serve as the foundation of this country.
Having an education system that is: (1) compulsory, and (2) completely detached from any sense of personal and legal responsibility on the part of the people involved (students, teachers, parents, etc.) is a recipe for disaster.
The failure of education in this country isn't that our schools turn out so many dysfunctional kids with no skills . . . it's that they waste a lot of money in the process of doing it.
I actually edited my post before publicizing it. I took out a short diatribe about why the government is even involved in education. The constitution does not provide education as a right or service provided by the federal government. This country can "afford" public education. But at a minimum it needs to be run by the states, completely devoid of any federal interference.
How's this? Let's "privatize" public education. Let big corporations run schools for profit. Let the government pay the "big corporations" based on the product. Have national standardized testing. The "big corporation" makes every teacher an "owner" of the school. They all get paid based on SAT/ACT/standard test scores and student improvement.
(I know it will never happen)