America is a continent, not a country

To add to the irony, "American" is probably the easiest and most correct demonym outside the USA. Something like "usian" will require other people to know English enough to understand what the "US" stands for.

"American" also doesn't clash with any other country's name (official or not). It would have been a different story if a significant number of people identified themselves as "North American" or "South American", but I don't think it's a thing?