It seems like after the Revolutionary War, the colonies didn't really care that much about each other's success. How united were they really? Was it likely, or even possible that they became individual countries instead of states of a single country?
In the long-term, it was unlikely, but in the short-term, it happened. The former is directly due to the latter.
The British Empire considered the U.S. to be the 'Thirteen Colonies' because there really were thirteen of them. As such, when each seceded, they were technically thirteen independent states, which then confederated into what we know as the USA with the famous Declaration of Independence.
The U.S. started out with a proto-constitution called the Articles of Confederation. It granted absolutely massive local autonomy, to the point of not even referencing the States as a unified nation but instead using terms like "firm league of friendship" and "each state retains its sovereignty, freedom, and independence".
The Articles essentially implied that the thirteen United States were all still independent - and with how much support was needed by those states to do... any of the things that a sovereign nation needs to do, that viewpoint might not be false.
The United States in Congress assembled shall never engage in a war, nor grant letters of marque or reprisal in time of peace, nor enter into any treaties or alliances, nor coin money, nor regulate the value thereof, nor ascertain the sums and expenses necessary for the defense and welfare of the United States, or any of them, nor emit bills, nor borrow money on the credit of the United States, nor appropriate money, nor agree upon the number of vessels of war, to be built or purchased, or the number of land or sea forces to be raised, nor appoint a commander in chief of the army or navy, unless nine States assent to the same:
Long story short, the Articles granted far too much autonomy to the states, turning the U.S. into as much of a disgruntled nightmare as the contemporaneous Holy Roman Empire. This national structure was doomed from the start, and would be replaced with the better-known Constitution just six years later.
After that debacle, the possibility for the United States actually consisting of individual sovereign states went down the drain. In that sense, the American experiment with statehood was a failure. Even today, there are issues with states having the autonomy they have. Debates over states' rights are still a thing.