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>> “ If I’m not misreading it, your belief is that the most important element of schooling is the religious portion and if a school does not include a large dose of religion it is a failure and leads to godlessness. I will point out that we have had public schools in this country since before we were a country, and the 1800s and early 1900s did not appear to be a particularly godless time.” <<
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And now I will point out what you appear to have deliberately left out:
Until the mid 1800s the US government printed Bibles for the schools, and that Bible was more than half of the curriculum, when our schools were turning out great men.
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What does Christ do with the lukewarm? Answer: He spits them out of His mouth!
Only in a private setting can children receive the non-generic and fully warmed up religious worldview ( godless or God-centered) that most closely supports the values taught in the home.
Government should have never flopped its big hairy toe over the line into the business of schooling. Why? Answer: Because education can never be religiously, culturally, and politically neutral. Such a philosophic state of neutrality is impossible in the mind of any sentient human. Those political factions with the greatest clout will get to control the non-neutral worldview of the next generation of voters.
In the 19th century Protestant Christians had the most political clout. Today, it is the secular atheists.