Our republic is successful because we had a culture that supported those values. The Founding Fathers had the advantage of being able to shape the political system accordingly. Without a republican-oriented culture in place as legacy from Britain, those great men would have been footnotes in history. Our founders would not have been able to turn any Islamic country into a successful republic because Islamic culture is antithetical to our republican ways. That's why "nation building" has been such a colossal failure. You first have to have a culture that supports republican values and then build a political system, not put a system in place and hope the culture follows.