I'm actually surprised that nobody remembers how the change originally occurred. In the late 80s when professors like Skip Gates was making a big splash at Harvard and Toni Morrison was the toast of the planet, a monumental book was published called the Norton Anthology of African-American Literature. Anyone who was paying attention would know and recognize that a new generation of scholars were getting a foothold in the better class of universities around the country, and Black Studies Departments were in the intellectual conundrum of only having a couple decades of history to justify their existence. The newer, younger, smarter black scholars in English for example would be quick to point out to people who didn't get it, that authors like Frederick Douglass didn't call himself 'black' nor did Jean Toomer. The expanse of interest in the 'black experience' had to be put in a more appropriate context. So the academic world rightly adjusted its terminology. To talk about the corpus of literature, music, dance etc of blacks in America, you couldn't just overuse Black America - so the term African American was used as a blanket term which was more academically proper, demographically equivalent and politically neutral. Americans of African descent thus became this in the abstract for the purposes of more accuracy - you could then put slaves, ex-slaves, free persons of color, Coloreds, Negroes and Black Americans all in the larger category and use fewer asterisks, anachronisms and other such malaprops.
Around the same time, a charismatic dude named Molefi Asante wrote a 50 page book called 'Afrocentrism' which kicked off yet another chapter in the African American history of mobility in identity. (See? I used it correctly there.) This could be thought of as a second, or third if you want to count Garvey, attempt at a Pan-African unity in identity. For a short time, I myself identified with an international jet-set of 'New World Africans' while living in Brooklyn partying with Spike and dating cute Francophone chicks from Senegal. I almost got into the kinte cloth business. But that was then.
I would gather that there are still a number of folks who are fascinated by the cultural dynamism of that international jet-set including the likes of Zadie Smith and Cornel West and all those who did Bring the Noise/Funk in those glorious early 90s, but Janet Jackson blew up and bifurcated the dreads from the crinkles and as far as I know, the twain never rejoined. By the time John Legend and Common went back to short hair, I think the whole Afrocentric thing was over, but I can't say with any accuracy because I went into the suburban daddy business. Suffice it to say, the whole African angle lost currency, especially for those who don't even read 50 page books.
I think it came as some surprise to some that we went through a period of Bone Thugs & Harmony after all highbrow folks went through, which is part of the reason Lauren Hill was such an incredible surprise, but I digress with these cultural touchstones to point out that your basic 'black culture' goes through many shades and degrees within the spectrum of African American history. I have made my peace with the fact that it's under no direction or control but rather a manifestation of who's following whom, a very personal choice.
I can't account for why people focus on race, when culture is so much more nuanced and interesting, then again, the politics of race in America is pretty much the same stagnant story, and like I said, a lot of people can't be bothered to read.