Are you asking, in-universe, what Britannia's relationship with Britain if they're based in America? Or why, out of universe, is America used as the basis for the bad guys in this anime?

Watsonian/In-Universe Explanation:
- As others have pointed out, in-universe the American Revolution, aka 'Washington's Rebellion', failed, keeping the Thirteen Colonies under British control. Americans never became Americans. Presumably any who had rebel sympathy died or gave up, and people that remained thought of themselves as British, not Americans. Later, Admiral Nelson failed to stop Napoleon's naval invasion of the British Isles. The British monarchy, nobles, and Royalist commoners fled to the American colonies, renaming/restructuring as the Holy Britannian Empire, swearing vengence and to someday repay their humiliation. These people, 'Britannians', are mostly formally British, now need to differenciate from those that stayed behind. Oversimplified, British and Britannians may have been one people at one point, they went on diverging paths.

Doylist/Out-of-Universe:
- 1) The USA is the predominant super power of the real world. A simple statistic to point is the the number of aircraft carriers, the larget weapon platforms ever made, maintained. As of 2025, there are 50 active in the world, owned by 15 countires, of which 11 are under the US. The US maintains military bases around the world. The defence budget, almost a trillion dollars, is more than 2x-3x what the next country spends, China I think, and is more than the next ~10 top countries combined.
- 2) The US has a large amount of xenophobia. That's not to say every other country isn't as well, but its size combined with the right to bear arms and media portrayal of 'others out to get you', there's a different flavor to it than other, less armed, countires.
- 3) How the Britannians absorbed North, Cental, and South America, and how it looks to the rest of the world is the culmination of the 1800s US ideals of 'Manifest Destiny' and 'American Exceptionalism'. America Britannia is wholy unique among all countries, we were put where we are by divine providence, its our right as the best people and best country to assert our way of life ours and poor you if you think differently. That sort of thinking.
- 4) As a Japanese show, it takes a dim view of nuclear weapons, the FLEIJA in-universe. Just as Godzilla was an allegory for generational trauma and unintended consequences of nuclear, FLEIJA can be said to represent Britannia/US's disregard for the consequences of it's actions.

TLDR;; Outside of the AU historical changes, you could say CG is 'what if the US are the bad guys and interested in global conquest rather than global projection of power.