A universal privatized system would bring the efficiencies of the market to a sector that badly needs it.
This is a myth.
The problem is for almost 30 years now schools were forced to deal with social issues and public policy that were originally addressed by local government social services; schools were thus compelled to address issues having nothing to do with education. We need to refund local government programs which deal with problems associated with poverty and violence and get schools out of doing social work and back to educating.
If schools are gubmint-run institutions, they will always be testing grounds for social engineering by politically motivated people.
As long as politicians have a nexus with education, then education will always be politicized.