For a normal, Judeo-Christian, Western, cultured, liberal-thinking population such as the one that existed in the colonies in 1776, yes, you are 100% correct but to compare it to the Egyptian masses seems like a very inaccurate comparison.
It is not just about the document and how it is crafted. IT IS ABOUT A MATURE POPULATION OF FREEDOM LOVING INDIVIDUALS READY TO ACCEPT ALL THE PRINCIPLES LAID OUT IN THAT DOCUMENT AND NOT THE DOCUMENT ITSELF.
You think the Arabs in ANY Arabic or Persian nation today are anywhere near the enlightenment of our 18th century forefathers? You think they are capable of signing such an amazing document with a feathered quill pen? I mean that pen is space age technology for them! 237 years ago, many of the colonists were illiterate. Today, the vast majority of the Arab world is illiterate and their leaders keep them that way.
It will take at at least another 500 years for the current Arabic populations on the planet in this 21st century to get somewhat close to the mindset of our 18th century forefathers and even that bet is a longshot! Happy Fourth!
It's the content of the people, not the document only.