As a teacher of American History, and specifically one who teaches history from the Age of Exploration to The Civil War, I have thought about the conditions and causes of the break-up of British North America.
A country sets up a colony for the purpose of the benefit of the mother country. While the initial explorers came looking for the "Northwest Passage" they discovered a land and sea laden with exploitable resources. The countries in best position to take advantage of such natural riches were Spain, France and Great Britain.
The British arrived first, in 1607 (okay, the Vikings were here first, in Newfoundland, but they kept their discoveries to themselves) and set up Jamestown.
Not to be outdone, in 1608, the French sailed up the St. Lawrence River and established the colony which we know today as Quebec City, and Montreal soon thereafter.
The British returned with the Pilgrims' landing at Plymouth in 1620, and the Dutch got into the act by 1624 when Peter Minuit bought the island we know today as Manhattan.
The Spanish had already firmly established their domain over the southern part of the continent in Mexico, and along the Gulf Coast of today's southern USA.
Each established colonies were shipping raw materials such as fur pelts, precious minerals, tobacco and cotton back to their mother countries.
It was all boiling down to who was going to ultimately be the dominant power on the continent. The British and French had been at odds with each other for hundreds of years before, so it was inevitable that they would clash over the new land. The British effectively overthrew the Dutch in a pretty peaceful transition of power in 1664, taking control of the New Netherland colony, and turning it into New York. It would take The British over another one hundred years and an alliance with the Native American Iroquois people to finally defeat the French.
In the mean time, the people of the British North American colonies were developing their own social, political and economic culture. Yes, it was based on British tradition and order, but it was far removed from it. And Mother Britain failed to recognize the people of the colonies as full-fledged British citizens.
It was more pronounced in the southern colonies than it was in Upper Canada (Ontario) or Quebec. The most brilliant thinkers to come from the southern colonies, people like Thomas Jefferson, John Adams, Benjamin Franklin, Alexander Hamilton, Thomas Paine, George Washington, and many others, realized that the destiny of the colonies would be better served in the hands of the people living there, rather than a disinterested monarch living 3000 miles across the Atlantic.
To "punish" the colonies, the monarch began taking interest and coming up with all kinds of laws and taxes to put the colonists in their place. Rather than creating an submissive, obedient colonist, it sparked more anger and led to revolution.
The northern colonies (Quebec, Upper Canada, The Maritimes) would eventually gain their independence through evolution in 1867. The southern colonies revolted and would declare their freedom in 1776. The war lasted until 1781, with the colonial victory at the Battle of Yorktown, and the Treaty of Paris in 1783.
For the now fledgling United States of America, the struggle with the British would continue for years to come, continuing with the War of 1812, and finally settling down in 1815, after the Treaty of Ghent was signed (and Andrew Jackson broke it at The Battle of New Orleans in early 1815).
If Britain had successfully stopped the revolution, I think the course of history would have looked different, but I believe that its outcome would have been similar. The southern colonies would have eventually continued to fight for, or they would have been granted independence. Perhaps, rather than a United States and Canada, there may have been one nation, united by their mutual interests and survival. The actual outcome resulted in two distinct North American cultures, Canadian and American. Both are rich and noble in heritage and tradition. The Canadians have their mixed British-French traditions. The Americans developed a culture as being the open arms to the rest of the world, embracing the traditions of many cultures, while developing one of their own.
I truly believe that history happened as it should have. The United States and the United Kingdom enjoy a close, relationship now. It took working out our differences then, to have the close and strong ties that we have. And that's my take on the question...