Home schooling well requires one parent to not work usually, and they also need to be good at actually educating; not everybody can do that. A lot of households have two working parents and a lot of parents are not qualified to teach. If you got rid of public education illiteracy rates in this country would skyrocket.
@Dexter Bass ackwards.
Out in the sticks, away from city ways, Women GET to stay home.
Children are still routinely home-schooled, and where the parents and grandparents might be unqualified, folks cooperate. Normally home-schooled kids spend far less time studying, and get far better grades.
And considering the high illiteracy rates and drop-out rates coming out of the public school system, I would say you are exactly wrong - That literacy and education rates would increase the closer you got to county/city/home controlled education.