The USA was not the first republic with a modern written constitution. That distinction goes to Corsica (if you don't consider San Marino's governance as "modern.") Corsica's constitution was, of course, heavily influential on America's; Alexander Hamilton founded a club called the Corsicans while still at King's College, New York (now Columbia.) Enlightenment ideals and progressive politics may be delayed but will not be stopped by a failed American Rebellion. We would likely see constitutional monarchies be the norm in the Americas, which would have both advantages and disadvantages, if Pedro II of Brazil and Maximilian I of Mexico would show.Thinking about how the U.S independence modelled the system of government of hundreds of countries. The constitution, the tripartite power, the elections, the parliament, the presidency, and all that stuff (the way they were put up in practice in the U.S) influenced almost all of Latin America and then Europe, Africa and Asia.
How would post-ARW revolutions happen and what governments would they produce? Would the world still be dominated by monarchs or would another alternative arise sometime, somewhere? How would we think the concepts of Republic, Democracy, Parliament, "Presidency" (it could be called other thing!), and so on. I think this might be one of the biggest effects long term