Regarding “USA” - when IRA stands for Illinois Republican Army, then that won’t be such a weak argument.
The “Great” is a bit much, but understandable seeing that it’s the only Britain, making it at the same time Great and Little. Perhaps something more along the lines of Hawaii to denote a handful of islands. After all, Japan was hip enough to drop “Empire” after WWII, even though the Emperor was still around and the Prime Minister wasn’t.
I will agree that the “A” could be dropped as a suffix to U.S., as it sounds like the U.S. is in control of all of North, Central, and South America. What I’m I saying – it is! I think the U.S. is the only country in America that’s subdivided into “states”. But to continue your “states” argument, each of those “lands” in the U.K. aren’t kingdoms, not even doms (a bunch of cons aren't called condoms), so how come uniting a bunch of lands turns them into a kingdom, which further argues why not United Kingdoms. AND, you currently don’t have a KING! Perhaps United Kingdead or United King-Once-Upon-A-Time or United Kinghuh?
Here’s a suggestion for those European islands, the United Been-There-Done-It.