DBWI United States of America Plausible version?

so i just got done reading a trilogy of books by S.M Stirling about a fictional nation called "The United States of America." Its POD is where the Rebellion of the 1770s were successful and an independent state is created. In the books, however, America is depicted as somehow expanding and dominating the North American Continent in a few decades, not to mention its status as a Mary Suetopia, completely democratic and everyone is welcomed in.

So i was wondering if anyone knew how to make a more plausible version of "America." What would happen in real life if the 13 colonies broke away and became an independent nation?
 
POD: William Pitt the Elder doesn't decline to enter the Lords and accepts title of nobility. Without Pitt in the Commons, lesser men make a real dogs breakfast of the American Crisis and provoke a war.

Here's what happens

1770 and 1780: After a prolonged conflict, the former colonies gain their independence thanks to aid from European allies and the use of guerrilla warfare tactics.

The new nation elects to form a confederation/federation similar to the United Dutch Provinces or Swiss Confederation. Let's call it the Confederate States of America, mostly referred to the CSA or America or the Confederacy.

1790-1820: The CSA spreads to the Mississippi. The CSA avoids the European Wars and this gains time to grow and expand.

1820-1840: The CSA builds its industry and population to over 15,000,000.

1840-1860: The CSA fights a war of expansion with the formal Spanish colony of Mexico and annexes New Orleans, the Mississippi valley, Texas, and all the land east of the Rocky Mountains.

1860-1880: The CSA begins the process of ending slavery.

1880-1920: The CSA grows larger and more powerful.

Slavery is abolished by 1890.

The CSA doesn't get involved in World War I.

1920-1939: The CSA endures a hard recession but recovers within a few years.

1939-1943: The CSA joins the Allies (Britain, France, Germany, and Austria-Hungary) against the Axis (Italy, Japan, Mexico, and Russia) in World War II. The Allies win the war and carves up the empires of the losers. the CSA annexes California and New Mexico.

1943-present: The CSA has been at peace since the end of WWII, with the exception of a few peacekeeping operations.
 
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I really, really doubt that the proposed united America would last. There are just too many entrenched cultural and economic differences between geographical regions in the colonies. Even if they did become independent through the rebellion, I doubt they'd last more than, say, 100 years before fragmenting into two or more separate countries.
 
the idea that you could have a republic on such a grand scale seems as frightening as it seems unlikely. If it did form I'd give it 20-30 years tops before political differences split the country across the middle.
 
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