"The current K-12 educational system exists, generally speaking, for two primary reasons. First, its scalability makes it easy for the state to educate its citizens, and second, it gives children and teens a shared public space where they learn to interact with others and hopefully pick up some societal norms."

This is completely wrong. The five functions of school are generally recognized to be Training, Sorting, Socialization, Caretaking, and FRPL. The author doesn't even get partial credit, because each function affects how each other function is implemented. So a school system whose only roles were teaching and socialization would have essentially zero in common with our school system today.

"Influential books in the un-schooling canon include Deschooling Society by Ivan Illich"

The thesis of Illich's book is (IIRC) that one of the biggest flaws of society is that each area of life is dominated by only a few major schools of thought, and these schools of thought tend to favor the elites. The book isn't even about education, let alone unschooling, albeit a lot of his examples are about education merely because it turns the title into a clever pun.

In any event, do you really want to be taking advice from someone whose clearly never actually read a book about education, or any of the vast amounts of research?