African/Asian/German/Martian-American doesn't make any sense as a descriptor of people who are third+ generation Americans.
We use African-American for pretty much all black people, but we only ever use Caucasian/Latin/Asian versions like German-American and Chinese-American for direct immigrants and their children. Even by that second generation, I have a hard time thinking of them as foreign most of the time.
I wonder why we say German-American and Mexican-American but not Niger-American, though. Mm.
Stricly speaking, I prefer to use the term black. I once saw a movie (I can't remember the name of it right now. dang) about two elderly (as in 100+) black women who had been successful during the heyday of segregation. The journalist interviewing them referred to them as African-Americans, at which point they politely (kind of) chewed her out for it, saying they were American-Americans. It stuck with me.
That's part of it, too. But I differentiate between that and direct immigrants and sometimes their children because they tend to also have been born in another country, so it does make sense to reference that part of their nationality, if you're going to refer to them by it at all. Moving to America doesn't instantly erase where you came from.