Jobs and culture are indeed reasons for people to move to the city, but it’s odd to claim that housing types don’t factor into consumer demand. Because housing types do, developers are incentivized to build housing that is the most profitable (such as less dense and luxury housing) not housing that best serves the needs of low income people (as more expensive units make more money). At best we can only expect minor effects from deregulatory mechanisms.
Which brings us to public housing. The main obstacle to public housing is funding these projects. Reasonable deregulation of public housing projects makes sense, sure, even though that is not the main blocker.
But public housing deregulation is not the argument of abundance, it’s YIMBY deregulation. Its proponents claim that it’s market based supply/demand effects that need to be unleashed by deregulation to provide adequate housing. Because “abundance” holds that YIMBY deregulation is the solution - not public housing - it misdirects efforts to address housing issues faced by low income people.
What YIMBY deregulation do you view as problematic? YIMBYs aren't calling for more billionaire row towers and multifamily to single family townhouse conversions. They are calling for more apartment complexes, ADUs, and other utilitarian forms of housing.
New housing developments only gets branded as "luxury" because that's the way that housing is priced right now. It costs the city of San Francisco over $1 million to build a single affordable housing unit. Blindly throwing more money at the problem doesn't help. SF is spending $846 million on housing, over $1000 per resident. Despite this, homelessness is actually increasing. Increasing funding is something that should be prioritized after you made development as frictionless as possible. If public housing is cheaper and faster to build, more voters would be willing to support funding it.
I gave SF a lot of shit, but to be clear, they're the least problematic city in the Bay Area, as they at least allow some denser development.