First, the conflict would be better titled The War of American Independence, as there was no top-to-bottom social upheaval seen in the French, Mexican or Russian Revolutions. Though there was a popular element ( especially in Massachusetts, where the revolt first caught fire) it was propelled and managed by the same elite that had governed previously. The various state legislatures/ assemblies selected delegates to the Continental Congress, and they were in charge before and during the war. After the war, that loose confederation of states continued, with no attempt by New York to, say, acquire Connecticut. And those state assemblies then , generally, selected their own equivalents to the exiled royal governors.

Although the new United States were quite weak, they had relatively little economic value.. The British made an effort to quash the rebellion for some years, but they were involved in several other conflicts abroad. They were far more concerned to secure their very profitable Caribbean territory from the military efforts of the French and Spanish to expand their own profitable colonies there, and they were just beginning to embark on the series of wars which would , in the 19th c., put them in control of India. Keeping Canada allowed them the prime fishing grounds of the Grand Banks. So, the defeat at Yorktown was not all that hard to forget.

As far as the Revolutionary War becoming revolution, there was once a common view that the Articles of Confederation period, 1781-1788, had been teetering on the edge of collapse into anarchy and armed conflict. The Continental soldiers had been paid with promissory notes that were initially valueless, and so there was a large, potentially restive population of men-at-arms. The public debts from the war were huge. Shay's Rebellion raised some fear of "the mob" taking control, especially in the minds of people like George Washington and John Adams. Before that could happen, it was thought, the Constitution was ratified and saved the new nation. This was very much the 19th c. view- especially for people who worshipped the Constitution. However, that view has mostly been dropped or greatly amended, now. Though there were structural problems with trade, and currency, and foreign relations, states tried to muddle along. Some of them tried to settle their debts, some of them were very slow to do so. Shay's Rebellion ( really a tax revolt) was quickly and pretty bloodlessly put down , but the political leaders who sparked it, by demanding hard currency for taxes, were voted out. Fears of Mob Rule seem to have been unwarranted. Notably, George Washington wanted to go home, be a gentleman farmer, and manage his slaves, not become a dictator.

Likewise, some have suggested that perhaps the Federalist Constitution might not have been inevitable, and with a few changes perhaps the Confederation of the United States might have been able to keep going. Of course, though the states might have bumped along just fine up until 1800 or so, it's hard to imagine how the United States under the loose structure of the the Articles might have made its way through the Napoleonic wars, or managed the War of 1812, and it is hard to imagine the country not dividing in half over the issue of slavery, even going to war over it sooner than it did in 1860.

Merrill Jensen (1959). The Articles of Confederation: An Interpretation of the Social-Constitutional History of the American Revolution, 1774–1781