No, I'm sorry but American is not the colloquial usage, it is the correct usage as defined by the members of that nation for the English language. Here is a listing of those names for the citizens of the countries.
There are other groups of would-be unions of states as well, such as the erstwhile "United States of Africa". The term united states is almost generic, while "of America" is the designator that sets this particular union of states apart.
To your point, American citizens have long emphasized the word America. Since the beginning, in fact: the original Declaration of Independence doesn't capitalize the term "united", calling itself the "unanimous Declaration of the thirteen united States of America" adopted by the "Representatives of the united States of America" on July 4, 1776.