That sounds backwards on both points. Poverty impacts how people perceive and interact with the world from building relationships to the use and conservation of assets. For example people in poverty are less likely to save for the future because institutions necessary to safely preserve assets into the future are distant therefore resulting in behaviors motivated towards immediate consumption. That is not something fixed by just throwing money at it.
At the same time social systemic unfair treatment can be fixed with money as it allows an otherwise well positioned person to alter their relationship with the constraints imposing such unfair conditions.
> So, if a poor white family is given a lot of money and they move into a richer neighbourhood, they would enjoy a social capital the same amount of money cannot buy for a black family.
That imposes a bunch of unstated assumptions that may or may not apply. Most all my neighbors are black families of different economic statuses who moved into a predominately white neighborhood and did just fine regarding social capital.
AA is not a poverty alleviation program. It is a social justice program.
Poverty alleviation can be done just with money, but social systemic unfair treatment cannot be undone with money. For example, despite owning homes in the same neighbourhood, the appraisal of homes of black people ends up lower than white folks[1], there are more traffic stops and searches for black folks than white[2]..etc., you get the drift.
So, if a poor white family is given a lot of money and they move into a richer neighbourhood, they would enjoy a social capital the same amount of money cannot buy for a black family. Now there aren't many ways to suddenly make this go away. So, AA is an attempt at making this go away by saying, put more of the people from the underrepresented community in places where they are underrepresented, starting with the high echelons of education. By that the society hopes to the laws we create, systems we build as a result will have the perspective of people from those community. It's not a silver bullet, not a magical solution, but one amongst many things to try.
[1] - https://www.nytimes.com/2022/11/02/realestate/racial-bias-ho... [2] - https://www.nature.com/articles/s41562-020-0858-1