The easiest way to provide affordable housing is simply to build more housing, and let the existing stock filter down due to the newly-increased supply.
The easiest way to provide affordable housing is to raise wages. You can do this by having a functioning economy. Unfortunately, depressed areas are depressed due to 50 years of sending jobs overseas. Right now, it's trendy to live in cities, so they're attracting the upper middle class. Eventually, the steam is going to run out of that engine, and we're going to figure out that a city full of nothing but bars and starbucks is a net drain on society.
A robust supply of housing is an integral part of building "a functioning economy". It's not just renters and future homeowners that lose out when housing supply dwindles; the surrounding businesses lose out too. People have less disposable income, meanwhile their costs rise due to having to support the housing costs of workers that need to live nearby.
