I concede. Your plan does seem better with one exception - don't illegalize homeschooling. I had trouble dealing with social interaction (I'm mildly autistic) for the few years I was in a (Christian) school, and struggle with some subjects but excell in others. Public school would never have been an option for me. I also gained a lot from learning to research and educate myself. It's the only reason I caught on to their bullcrap doctrine, learned Nietzschean philosophy ( which helped me make sense of a world without "god"), etc.
I propose an alternative:
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Homeschool curriculums must be state approved, including the individual books - not just the subject branch.
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No religious text, textbooks based on religious doctrine, etc, may be included in the curriculum.
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The child has the right to reject a curriculum choice, and defer to the subject curriculum used by public schools in their district (this will likely only work for highschool of course, hence state approval also being required)
How do you think this would work as an alternative?