It's impractical to simply abolish the public schools all at once. It'll take a weaning off process to accomplish a complete disconnection of the government from primary education. I think it could be done, but that's a bigger conversation.
Everyone who says that we should privatize all education should be forced to spend 2 years in a country without public education. They do exist, but you won’t find a single one with an illiteracy rate that isn’t heartbreaking.