Research shows that integrating poorer families into healthier, mixed-income neighborhoods has improved prospects for them and their children. A prominent Harvard study last year found that young children whose families had been given housing vouchers to move to better neighborhoods were more likely to attend college — and to attend better colleges — than other children, and had significantly higher incomes as adults. This form of economic integration could be crucial to breaking the cycle of intergenerational poverty.

By describing efforts to achieve integration as “social engineering,” Mr. Carson seemed to suggest that segregation was a natural element of civic life. It is, in fact, very much the consequence of decades of federal policies. Chief of among these was the system of private mortgages guaranteed by the Federal Housing Administration, which did much from the 1930s to the 1960s to promote homeownership for white Americans. But the agency discriminated against black citizens, as a matter of policy, and insisted on black-white separation in housing.

The Fair Housing Act of 1968 was supposed to end all that. But meeting fair housing goals has been well down the priority list of most housing secretaries, and the rules have been spottily enforced.

One important thing for Mr. Carson to understand is that enforcing the law, and making sure that state and local governments actively pursue economic integration, will help whites as well. Low-income whites make up more than a third of the 4.6 million poor families that receive housing assistance through HUD. They will also benefit from broader access to housing in healthier communities with better schools and job opportunities.

That point is beginning to hit home with both Democrats and Republicans in Congress. The House speaker, Paul Ryan, in an antipoverty plan he released in June, called on the government to make housing assistance vouchers portable so that recipients could move “up the economic ladder” by moving to places with better education and job opportunities. Last summer, both houses approved a bill that insulates low-income families from rent increases that could push them into homelessness and also expands their access to housing, jobs and schools in mixed-income areas. The Senate blocked a bill that would have stopped HUD from enforcing the rule requiring it to pursue fair housing goals.