I have found United Statsians (I love that name) have adopted 'American' as their own and that they do not readily share it with others.

We take that title because it sounds so much nicer than United Statesian and we're the only country whose name actually has the word "America" in it. It would also be somewhat absurd to call ourselves "United States of Americans". Plus, every other country in the Americas seems to have short, concise names that. The United States of America isn't really that creative of a name anyway, and since there could be a United States anywhere, we use "Americans".