Not government control but control by the parents,
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I would agree, if this means that a group of parents voluntarily get together to hire a teacher ( with their **own** money), rent space, and open a school.
Most definitely, parents should be the primary educators of their children and control all aspects of it. They, after all, care most about the future of their children.
I was thinking the model of co-op non-profit nursery school where the parents hire the teacher, rent a place, and also sit on board of directors and decide the curriculum.