These are ironically the weakest counterarguments to abundance housing. Rich people don't move to a city because of their love of 5 over 1 buildings. Otherwise, developers could just build them in rural Kansas and everyone would be happy. They move the jobs and culture, which doesn't change regardless of any new housing built. Making it easier to build privately owned housing also makes it easier to build publicly owned housing. Public housing projects are also delayed by permitting and environmental reviews and have to pay for inflated land prices and parking spaces.
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.