There are a bajillion problems with the "garden of towers" model of low income housing (or really, just housing in general - middle and even upper income projects following that model have largely also failed, though obviously without such disastrous outcomes).
Stuy Town for example is an example of this model being applied to middle and upper-middle class housing, and it has similarly failed to produce the communities they were originally intended to, and are now more known for being inaccessible and cheap than desirable in any particular way.
The modern model in NYC for low income housing is to mix them in to market-priced buildings, and either subsidize the building directly or offer indirect incentives (more height limit and buildable floor area being the big one). IMO this works a lot better, and is at least closer to what Jane Jacobs IMO correctly identified as a critical element of making cities work (the geographic mixing of economic classes).