Your post, there are no Mexican Americans is very good, except things change. There are no Mexican Americans in history, but there are Mexicans today (in Mexico) and Mexican American today (in the U.S.).
From what I can tell, the emergence of a national (but not ethnic) identity of Mexico is real and all Mexicans are proud of the country’s rich history of pre-Columbian tribes, the colonial period, and the national period.
I think we conservatives would say the same thing about our country. American isn’t an ethnicity but it is a national identity that embraces our rich history. It’s the liberals who want to turn us into members of so many tribes.
With regard to being a hyphenated American, I suppose first generation immigrant have one foot in their country of origin and another foot in their country of choice. But I would be disappointed if second generation have such divided loyalties. In this view, there would be some Mexican Americans and they would either be resident aliens or naturalized citizens. In my view, Susana Martinez, having been a natural born citizen, is an American. Same thing with Ted Cruz.
I am an Angry-American.
I believe that because of American Exceptionaism, Americans are a race. I believe, and you’ll never hear any media outlet or bureaucrat say this, this country was founded and established with our constitution specifically for such an enlightened individual that he or she is indeed a new race of people created from Divine Providence.