In that situation, the problem has to be solved on the level above. The State as a whole should pay the cost, since it is the State as a whole that would benefit.
And people in suburbs will just get free cheque from government to move? That is incredibly unfair to people living in cities hence it creates moral issue.
If not, it is not more unfair than when health insurance uses the money of healthy people to pay for treatment of sick people. Or when the Federal Government uses the money of people who live in the mainland to pay for hurricane relief for people who live near the coast.
Where do you stop? Should a family of four (two young children) that lives in a 1 bedroom apartment in city be given a 2 bedroom apartment by the city government? They obviously need it.
I agree with socialised healthcare and education. First one because health is not some thing you choose but is affected heavily by genetic lottery (yes unhealthy lifestyle is a problem but it’s hard to objectively quantify) and second one because it means levelling of the opportunity field for young people not born to wealthy parents (again this is related to lottery of birth, what kind of family you are born into).
But housing is very different from healthcare and education.
Sick people are less productive. Uneducated people are less productive. People who are stuck on a dying suburb where there is no business and there are no jobs are less productive.
Can't they move somewhere else? They can't because it costs money. Why can't their government just give them the money? It might be cheaper than their infrastructure costs.