Canadians and Mexicans do call themselves Americans as do people in Central America and South America. They actually get mad about U.S. citizens calling themselves Americans. You really need to do some research.
No, they do not.
Most people associate with the country they are citizens of and that’s how they are known. Associating with a continent is not typical.
People in the USA (last word America) became know as Americans. What should they have called themselves? Staters? catchy.
If you’re in Canada, you probably associate with Canadians, as we know they do.
You see, there is a simple explanation for the use of American to be associated with citizens of the US. If Mexicans want to call themselves Americans, let them sell it to their citizens (the ones who remain) and other countries for that matter and stop whining about what the USA is doing.