In the English speaking world, North and South America are considered 2 separate continent, and the single word American is universally understood to refer to citizens of the United States of America.
We have referred to ourselves as American for over 200 hundreds years and we are the only country with the word America in the name.
In the English speaking world, there is no continent called "America" there is only North America and South America. If you want to refer to both we would normally say "The Americas" or maybe "The New World".
Since there is no "America" commonly used in English other than the country, there is for all practical purposes, no ambiguity.
Use is what gives language meaning, and if you look at the numbers "American" is almost always used to mean a resident of the US. Attempting to force a fix on a perceived issue is never going to work.
By the way prescriptivists have been trying to force manufactured demonyms on us for years and none of them have ever become mainstream.
I've met several South Americans who insist that they are "American", but after investigating further, even in South America, the word "American" is almost never used in English to refer to people who come from what we call North and South America.
When you think about it why would anyone want to refer to themselves as basically coming from the Western Hemisphere? There is no shared language, no shared culture, no shared government. It would be like saying "I'm from The Old World", when that applies to people from France, China, and Zimbabwe.
It's pretty much a useless distinction. And language use patterns back that up.
It does invalidate the original meaning because no one uses America to refer to that landmass anymore (in English). Common use is what determines the meaning of language.
"Nice" used to mean simple or foolish, "Silly" used to mean blessed, and "Awful" used to mean worthy of awe--modern usage patterns have invalidated their original meanings in modern use.
>I understand that it's not ambiguous to many people, but it's ambiguous in my own mind because I do think of "America" as applying to the entire land mass.
And I think of Columbia as an alternate name for the US. It doesn't mean I'm going to get on a Colombian Spanish language forum and start making up new demonyms for them.
Mexico City, Mexico.
Belize City, Belize.
Panama City, Panama.
Djibouti City, Djibouti.
See also: BRICS & recent political turmoil in Brasil, Ukraine