Zoning that allows higher density may and likely will result in lower housing prices in NJ, but that’s not guaranteed in Manhattan or SF or Vancouver or Toronto. In those places if the zoning changed, the developers of new multi-family housing will likely build luxury condominiums instead of rental units (and especially instead of affordable rental units). The NIMBYs you describe can be a problem, esp. in San Francisco, but take them out of the picture and what remains in desirable global cities are greedy developers looking to sell to fat cats.
Reading the article about NYC, the addition of new housing stock has driven prices up for everyone, including renters (esp. those whose landlords are PE firms).