I think trying to compare the history of Asian Americans and the history of African Americans is pretty difficult with dramatically different histories. (Rant Warning, might edit to cut it down and clean up as it's typed on a phone.)

There isn't any real answer to your question, but one can speculate with an understanding of black history/culture.

I'll submit one for your entertainment and I'm genuinely willing to discuss more possible factors with you if you're interested in theorizing: African Americans haven't been able to develop a culture (collectively) that is able to place value in the familial unit, pride in oneself, for one's people, etc.

When I think about the history and culture of all American peoples, there is one glaring feature missing in African American history: roots. There is no sense of cultural roots. Slavery, along with history in general, time, and other events, destroyed the average black person's connection to the past, to their family's past. (My family has tried to trace back our history and has only gone back no more than 150 years to a guy we barely know anything about.)

Could it be that without any sense of roots or legacy, blacks are less likely to have a sense of duty to continue or start said legacy?

But if you think roots and legacy aren't everything and familial value could be developed elsewhere, I think I'd agree, but also submit another factor. This lack of roots and undeniably constant sabotage of the black community makes it difficult to establish a culture. Which isn't a problem, culture doesn't have to be developed, it can be adopted, but there is nowhere to adopt from. I have already mentioned the severed ties to any possible African culture or values. The only other culture that can be adopted would be around them, but the culture African Americans were surrounded by, ie (general) American culture, is held by the same people that actively rejected them explicitly up to a few decades ago.

The point of all of this is: values don't come out of thin air. They have to develop with culture, but culture doesn't come out of thin air either. It has to take root, and there has been neither the time nor the conditions for this culture to take root.

I'm not saying this is the answer to your question, but it's something to keep in mind. I'd say every American ethnic group has something they can look back at and say "This is mine." Asians can look back on their respective countries or their immigrations. (Immigration stories are always inspiring, in my opinion. "My grandfather came to America with the clothes on his back and made something of it...." and all that jazz.) Whites can look at their European history or just know their family as apart of American history. I look back at my family history and anything of any importance is just a struggle against oppression. Anything before that doesn't exist. I could probably tell my ancestor's immigration story, but you've probably read it in a textbook already.

EDIT: Just a reminder that I mean just about everything in the general sense. For example, not every Asian/White/Whoever can or even wants to have a connection to the past. It's more about the culture that has been built out of it, regardless of individual connection.