One might conclude that was what our Founding Fathers envisioned.
There are some good arguments to be made for that, and why the Constitution was as secular as it was.
I might have put a purposeful salute to the Christian view of God in the Constitution, but as well a promise that nothing specific will be required of unbelievers simply because it is Christian. But I can’t hop in that time machine, so we got what we got, which was flawed.
The only real purification of such a situation has to come from above. We can’t pen it into any official document. God has to pen it into our own lives.