The problem is not with income as much as costs. The NIMBYism of a lot of places inflates the cost of the main expenses like rent - where most people's money goes - and the cost of getting around, as people are forced to live further away from jobs. That was the big finding from the minimum wage hike in Seattle, that poor people where forced to travel further for work, and it cost them more. Ironically, I think that is pretty much how all cities work since crime went away. The days of the poor occupying prime real estate near a city is pretty much over.
Even sans better employment opportunities, fixing the zoning laws in most cities would lead to better lives for many people. Sadly, this NIMBYism is really hard to fight against, and often the people it hurts fight hardest for it.