Surely, though, the organisation of cities into relatively desirable wealthy areas and undesirable slums is a result of the preferences of those with the power to decide, and not the disadvantaged "refusing to integrate" into areas where, by design, they cannot afford to move?
Marginalised groups don't control their own diffusion through the population, or their assimilation. It's not about human capital so much as it's about plain old capital.
The outcomes of the real estate market express the aggregated preferences and purchasing power of all buyers, resulting in the stratification of cities according to wealth. You see this occurring everywhere—the question is whether it needs to be regulated, and if so, how. Wealth concentrates through the consequent recirculation of social capital through personal connections, prestigious schooling and the like, which are themselves racialised in weird ways (cf that statistic about the composition of the Antwerp police force).
Piketty's empirical study of US income data (confirmed by less thorough analysis of other OECD nations) indicated that people with wealth tend on average to gain faster than those without it, except in times of upheaval. Demanding that the less wealthy as a group must possess the "human capital" to overturn this tendency is as unscientific as denying climate change—it simply does not happen.
Why do we accept "immigrants [of X type] don't integrate" narratives that hold the marginal to account for dynamics out of their control?