There are many aspects of the federal government that should be privatized. Schooling is one of them, but health insurance and Social Security should be taken care of first before anything else. Private contractors are in better positions to do a lot of things because they aren't limited by certain laws.
Yes, private contractors are in a better position than the government to provide quality schooling for students, because government workers are complacent. Anyone who has ever waited in line for a driver's license cannot possibly believe that the government can do something as well as the private sector. Private workers care more about their work.
If a teacher starts out producing good students, but for some reason become irrelevant or incapable of producing at the same levels, regardless of the reason, the contractors can just not renew a contract. This flexibility ensures that the teachers they hire are operating at peak levels. Government education facilities have become bastions for teachers that no longer have to teach effectively. They simply need to provide the content required.
I think in a private environment where teachers are held to set standards will push those teachers to provide a higher educational quality to students, I think in a public environment teachers can sometimes become lazy and content then it's hard for an administration to fire them after they achieve tenure which lowers the standard of education.
The educational system, whether in the form of private or public schools, is deeply flawed no matter how you slice it. With public education, at least you get some sense of a shared responsibility for the quality of education, whereas through private education, the disastrous pay to play frame will only further degrade our humanity. In either case, kids are being trained to be servants to a corporate state that is both corrupt to the core and hungry for war. The fundamentals of education must be re-examined altogether.