"Why would one think that "people of color" implies that standard "people" are white? It counterbalances "white people," not "people."

Because it marks everybody-who-isn't-white as being in one category, and whites in the other, unmarked one; the impression is People are white, people *of color* are need to be specified because they aren't, quite, people.

I'm wouldn't start calling myself Native American, though I probably have more Cherokee than some of my fellow-citizens have African...

Oddly enough, as a kid, I wasn't American, I was European, as in, the Europeans among us tonight are from the United States.