Americans are proud to be "hyphenated Americans". There are Norwegian-Americans, Irish-Americans and many others. Curiously, you don't hear of French-Americans, yet there is at least one whole community in Florida whose main language among themselves is French. The communities reflect historical fact, that whole lots of immigrants immigrated together and settled together, and their descendants have preserved the customs , and often,indeed, the language, of their ancestral homeland. Even when separated from areas of the original settlement, such people still retain the feeling of belonging to that ancestry and culture.
African-American is an attempt to replicate this and disown names with racist overtones, but it is strangely synthetic. Most came from West Africa but their ancestors would not, necessarily, have had anything in common: different tribes, different languages,different cultures, but the same fate. Martin Luther King referred to 'the ***' in his "I have a dream" speech, but that may not be acceptable now, in any context. 'Black' seems to be avoided by white American news anchors and in the press there, but freely used by African-Americans,