Yes, we should consider the United States as multiple countries put together, because it would do a great deal of good in helping the people remember that state's rights is so important. By remembering we are separate countries, the federal government would not be as large as it is today.
This is a problem and a bad way of thinking. While there are state laws, and things do shift culturally from state to state, we are all under one US constitution and in one union. The United States. It isn't the Assembles Countries of America and should not be considered that.
The United States can be seen as "E pluribus unum" or "One from many," but we aren't really separate countries. We have many regions and many states, but we aren't 50 countries put together. The United States isn't just the sum of its parts. The fine balance between the states' rights versus federal rights is part of what makes America great.
It does not make sense to consider the United States as multiple different nations. The United States is an individual, sovereign nation with a strong centralized federal government. Without the operation of a federal government, the country would likely descend into chaos and fracture into multiple countries, but as it stands currently, the U.S. is a single nation.
I think that while a lot of states in the United States almost seem and govern like they're their own country, I think the USA is still ideally a singular nation. While there may be differences of ideals and opinions from state to state, each state still believes in the principles of the country.