In some languages, but not really in English. Convention in the cultures of the Anglosphere is that the world comprises seven continents, and the Americas comprise two of them, not one. And in English, both formal and informal, “American” is generally considered the demonym of the United States of America, not the Americas. Although I call myself estadounidense in Spanish (an odd term—why don’t people from Estados Unidos Mexicanos count?), the equivalent English term is “American,” not “United Statesian.”

Not in English.

And USian could refer to folks from Mexico (and at prior points in history a number of other countries), so it's hardly unambiguous.

I'm citing a rule, not making one. American is in the dictionary, used by the UN, recognized by everyone and their dog as the proper demonym for citizens of the United States. Who are you to question that authority and replace the proper demonym with a neologism?