When people with middle or higher income move into poor neighborhoods public education improves, crime rates drop, and the earning potential of low income people living in the neighborhood before the gentrification goes up.
Some low income people object because of rising prices and rising property values increase rents and mortgage costs. Policies to help people who have experienced local price inflation, and rising property values (to the extent that the increase is unrelated to any improvements they may have made on their own property) to afford rent, mortgage payments, and the cost of living could mitigate the problems associated with gentrification, leaving mostly positive benefits.
Socioeconomic segregation is a serious problem. If everyone is poor in a large area then that expectation of remaining in poverty will be communicated to the kids growing up in the neighborhood. You even have schools where the culture is anti-success and kids will be bullied if they are trying to succeed in schools.
As people don't expect to succeed through legitimate means that can also mean greater crime rates.
Furthermore, rich people living in just rich neighborhoods become blind to the problems of people in poverty.
To remedy this the government should offer housing subsidies and tax credits for people who move into a neighborhood when and to the extent that moving into that neighborhood makes the neighborhood more socioeconomically representative. This should go both ways, encouraging wealthy people living in wealthier neighborhoods to move to poorer neighborhoods and poorer people living in poorer neighborhoods to move to wealthier neighborhoods. The poorer people should get more assistance in this case, because they will need it more just to be reassured they will be able to afford the transition.
The less separated people are by socioeconomic status the more aware poorer people will be of the opportunities available in this country and the more aware wealthier people will be of the challenges faced by others in this country.