(It was also a political marriage of convenience because in the '90s, railing against welfare was in vogue, and HOPE VI generally did not result in 1:1 replacement of public units, so it was a backdoor way to reduce the population on welfare.)

I don't really think the issue is density. Plenty of low traffic, low density suburban areas have high crime as poor people move into the suburbs; public housing had few eyes on the street because the design intentionally kept out passersby, and if anything suburban neighborhoods with high walking distances, mazelike streets and inconvenient, unpleasant walking environments are more extreme than that, and also have lower amounts of residents to boot. At least in NYC (and probably true of a lot of very inner-city housing projects) the towers in the park usually replaced existing urban neighborhoods at far lower densities than what had previously existed, because so much of the land was just idle greenery (that usually wasn't useful, in the form of small, segmented lawns often fenced off). Compare that with, say, Vienna, where the masses are housed in public housing in large midrise (5-10 story) buildings.

Coincidentally, this large midrise form factor is also what dense gentrifier buildings look like in many cities around the US, from Seattle to DC.