Here's a question that never gets asked:
If the purpose of displaying the Ten Commandments in public buildings is "historical," where's the history? Where is a single objective piece of evidence that provides a historical context or the most tenuous support for the establishment of the Ten Commandments?
We can verify aspects of, say, Egypt's legal system, or the Code of Hammurabi. We have contemporary Roman records that confirm at least aspects of the Gospels. There is concrete evidence of these things. Jesus is mentioned by Josephus, for example.
Not so the Ten Commandments. There is not a shred of outside evidence that any aspect of the story of the Exodus is true. As pointed out by John Romer in Testament (which I'm referencing from memory), a plague that wiped out the first-born children all at once is the sort of thing that the Egyptians made note of, especially when preceded by nine other anomalous disasters. Yet nothing in the various surviving records of the Egyptians confirms any portion of the account in the Bible.
We have the word of the Bible, and nothing more. Moreover, the Bible tells us that God himself handed the Ten Commandments over to Moses. That doesn't strike me as a strictly historical narrative. As a contrast, one can report with historical accuracy that both sides in the Civil War routinely invoked the Almighty -- one cannot assert with historical accuracy which side the Almighty actually took.
Here's another question: If these displays are "historical," why are their supporters prostrating themselves in front of them and praying fervently? I'm referring here to the reactions in Alabama as Roy Moore's defacement of public property was removed, rather than the particular monuments in Texas and Kentucky. But the question stands. This is not the sort of behavior that accompanies examinations of historical fact. Heck, even on the Fourth of July - for which there is ample historical evidence - all we do is eat hot dogs and watch fireworks!
But let's assume for the sake of argument that the Ten Commandments are historical. Does it automatically follow that they are therefore among the foundations of our legal system? Why is it that no other Western society - all of which have similar prohibitions, all of which draw on the same body of knowledge of the ancients - feels compelled to trumpet the Ten Commandments as the foundation of their system of justice? Did not every society have prohibitions against murder and theft and adultery? For if you take out the overtly religious commandments, that is all you are left with. For that matter, how can anyone present the first few commandments concerning whom to worship and in what manner as anything other than overtly religious?
The Founders knew their history. They were schooled in the Bible, certainly -- they knew it better than most of those who claim this is a "Christian nation" -- but also in Greek and Roman history. They read Herodotus and Thucydides and Homer and John Milton - and John Locke. The history that concerned them was that of the Roman Republic, and Athenian democracy - they were keenly aware that what they were attempting had been tried before, and had not survived. The history that concerned them was that of other European nations that had been riven by religious conflict. These were the things they kept in mind as they labored to create a government, not the Ten Commandments.
One last thought: The guys at the Constitutional Convention were mostly lawyers. They were constructing a legal document, using legal language. That means their use of language was careful and precise. Where they were not precise, that was by conscious design. (Use of the word "slavery" is carefully avoided, for example.) Had they envisioned a "Christian nation," they would have clearly said so. Instead, their only words on the subject are an unambiguous declaration that religion is never to be within the purview of the government.