Many Kings, some of whom were the most abhorrent people to grace the face of the earth, were given great coronations in the name of God! Did that make their Kingdom’s Godly?
The Bible is just a book, until we the people put the Word, within, into action. I look at the U. S. Constitution in the exact same manner.
Putting the word “God” on, or in, something doesn’t make it Godly. You obviously think differently.
I agree that simply slapping God onto the Constitution does not make this a Godly nation. Britain still recognizes God, Scotland still claims to adhere to the Westminster Confession but obviously this alone doesn’t make them Godly nations. In fact their actions suggest otherwise.
However what the Constitution does is explicitly say this is not a Godly country. The very first line makes that plain when the founders decided that government was ordained by “we the people” rather than God.