No. Housing projects lead to nothing but misery and more homelessness.
The increases are almost 100% drug-driven. Because of drugs, people are not _exiting_ homelessness (the average time of being homeless is growing, according to the 2-year counts).
The answers, counterintuitively, to strengthen the NIMBYs and make sure it's impossible to build ANYTHING in cities. Then promote the remote work and suburbs/rural areas via tax incentives.
The US has millions of square kilometers of perfectly good land available for housing. There's zero reason to try to cram people into the Human Cube ( https://www.syfy.com/syfy-wire/the-human-cube-the-volume-of-... ).