I don’t think anything single thing that tries to tell the story of Pruitt-Igoe captures it, because most of the failing are so embedded in the broader system. Things that tell the story of Pruitt-Igoe or Cabrini Green or Outhwaite tend to get too caught up in architectural determinism. There’s an old EPI article that is a really good start, because it carries a bunch of the background on residential segregation, slum clearance, and public housing in St. Louis, including both national policy concerns and local specifics. Everything up through section 4 is relevant, but 5 and 6 are just worth reading.
Outside of that I think a look at the major laws, or at least their Wikipedia articles is a good next step.
The housing act of '37 and the USHA it created, specifically the requirement for an income gap it required between the bottom of the housing market and the top of public housing incomes.
You also want the housing acts of '49 and '54.
When you piece them together the quick idea is that we created a system that only accepted the absolute lowest incomes. This often required social disruption because neighborhoods were destroyed and families would have to break up to clear income and work requirements. Once in these buildings we required that the rents of those, by definition, lowest income individuals had to cover all maintenance. We then required lowest cost construction, rather than a focus on durability or livability. Once we did that we built high rise towers that were lower construction cost, but extraordinarily high maintenance costs. This led to a rapid decline and all of the social ills that come with massive unsupported poverty. We built a nightmare machine.
