re: The problem is...
"The War of Independence was certainly justified, although Canada's example suggests that if it never had happened we would have gotten our freedom from Britain anyway."
More likely that without American independence, Canada would not gotten it's independence [nor India].
America not only got it's independence, but allowed the possibility of other countries getting theirs- it changed the way people looked at the world.
And btw the French would have never sold their American holdings to England, and Texas and other states may have aligned to other European powers- probably WWI and II [III, IV, and V] would been fought on the American continent.