How ironic that you try to argue the illogical nature of the term Americans, and then proceed to assert that there is some right way to spell words in one of the most illogical languages ever. Spelling in the English language is essentially arbitrary. Learn another language, and you’ll be shocked at how terrible of a language English is.
Finally, American is the accepted name for people from the US. Get over it. The world’s vernacular dictates what’s right, not you. It’s not illogical either, as the country’s name IS United States of America. People seem to think that that name means that we’re a bunch of united states who are the region known as America. That’s wrong. We are a bunch of united states that are collectively known as America. You will never, ever hear the “Western Earth” (for the record, the West refers to European-based countries which include, but are not limited to countries in North or South America) described as America. It’s is the Americas. There is North America; there is South America; there is the Americas. These are all references to continents or a collection of continents. America refers to ONE thing: USA.