Well, dubbs, the obvious answer is because the forefathers and many of the colonists grew up around Judeo/christian values; they weren't as well versed in world events and cultures as we are now. There is no reason whatsoever to turn towards religious texts to define the frameworks of a nation anyways...you'd look towards Hammurabi's Code and the Democratic practices of the Greeks and Romans first.
I'm sorry, but the concept of "Kings" is exactly what the forefathers were drawing away from. Just review the coronation of Kings and Queens in England, France, and Spain, plus review their ties with the strongest church in power at the time of their rise to power. Your logic isn't really coherent in your last statement...sure, you can Believe that, and they themselves could have felt that they were urged on to Declare Independence from England from something higher than themselves (extremely unlikely, when regarding the Deist and Theist beliefs), but their purpose and intent was to create a society promoting both freedom of religion and freedom From religion.