If Canada Had Never Been Invaded

 Some time ago this speculative question appeared on Quora:

"How would the United States be different if Canada was never invaded?"

I gave this as my speculative history answer and welcome other speculative analyses in comments :

"What is now Canada was invaded three times:

1. "When under French control, by Britain with full support of the American colonies. This was a successful invasion that resulted in British North America, eventually Canada. If this invasion had never happened, the American colonies would likely have remained sufficiently wary of the French presence that the American Revolution would not have happened and the United States would not have come into existence, remaining British colonies until eventually evolving into into independent nation(s) with full membership in the British Commonwealth of Nations. The Royal Proclamation of 1763 would have remained in effect and the American colonies would not have expanded across the Appalachians.
2. "During the American Revolution, by American forces that were completely repelled in successful defence of British North America. If this invasion had never happened, American revolutionary forces might not have suffered some depletion, General Benedict Arnold likely would not have changed sides, and the American Revolution just might have taken less time.
3. "With the War of 1812, by American forces under the official American federal government policy to annex British North America, a dismal defeat for the United States as the invaders were successfully driven out. If this invasion had never happened, it would be because the Monroe Doctrine did not exist, The United States was not as expansionist as it actually was, the War of 1812 did not happen, and there would have been no Treaty of Ghent (betraying British Ally, Tecumseh) to give Americans excuse to cross the Appalachians. The United States would likely have remained confined east of the Appalachian Mountains as Britain enforced the Royal Proclamation of 1763 to support Tecumseh in creating a viable First Nations confederacy south of the Great Lakes as a British protectorate and eventual independent majority First Nations nation state with full membership in the British Commonwealth of Nations. The United States would likely not have been in a position to purchase the Louisiana Territory from France, resulting in an eventual French influenced but largely First Nations nation state west of the Mississippi River. Spanish/Mexican control of what is now southwestern United States would have persisted and Mexico would now be a geographically larger country. The eventual British exploration and colonization of the Pacific Northwest would have kept a larger portion of that region under British control, extending between what would have been Spanish/Mexican California and Russian Alaska. The United States would not have been in a position to purchase Alaska from Russia but Britain/Canada might eventually have done so. Hawaii would never have become American, remaining a British Protectorate kingdom until eventual recovery to full independence as its own kingdom within the British Commonwealth of Nations."