Good luck getting commie blocks pushed through planning approvals today. NIMBYs in general are violently against any kind of public housing.
It’s more complicated than that. I’m massively pro public housing. I hate living next to it.
A poorly managed emergency housing facility is just a shit show. Violence, noise, rubbish, human and animal abuse, property damage, police attendance, debt collectors, smell, rodents, animal attacks, threats, overgrown plants etc, all within the last year, at my neighbouring house. If it was ever managed properly, people might view it differently. Managing it costs money, and then people oppose the cost when it doesn’t come with more housing.
No, they aren't. They are generally run by local housing authorities with state and federal financial participation, and, in any case, there have been basically no major new public housing projects in the several decades, with many existing projects decommissioned, and public housing assistance shifting from project-based to tenant-based vouchers.
Traditional government housing projects started falling out of favor in the 1950s and 1960s as the new projects were often both viewed as worse than the slums they were supposed to replaced and failed to even replace most of the housing units that were destroyed in the urban renewal efforts that created them, and support for them was essentially completely halted by the Nixon Administration in 1973, though it is possible (though, again, rare since the 1980s) for project-based subsidized housing to be created under Section 8, as well as the (far more common) voucher-based aid under Section 8.
The world is larger than the US - state and federal level public housing can be done and it can be done well, and at a scale it's only way it can be done. The fact it hasn't in the US doesn't mean it's impossible.