Britannia at all was begun by the British government moving to the American continent. After which said continent effectively became Britannia. If there's a critique of imperialism in it, Britannia's imperialism resembled the British and various European empires' rather than American-style globalization.
In the English dub, at least, there are actually some parallels between the Black Rebellion and the American Revolution: the Brittanian Emperor says "all men are not created equal" while America's Declaration of Independence began by saying "all men are created equal", and the new nation Zero forms to fight Brittania is called "the United States of Japan" but this is a common title. "United States" is a fairly common governmental style — Australia and Mexico, among several others, can be classified as United States — and doesn't specifically indicate anything about America.