Yes, NYC housing is very expensive, but that's because Manhattan is the most densely populated island in the world having a population greater than 150,000 people. Yes, you can squeeze a few more people into NYC proper, but there are physical limits that cannot be overcome, and New York is as close to those physical limits as anywhere else in the world.
The New York metro area does not have those same physical limits, and is much more dynamic than California with regards to new construction and real estate sales—at all pricing levels—as a result. Yes, as you get closer to Manhattan things get more expensive. But Manhattan is not the only housing option for people—even for people who don't own a car.
I live and work in a town of ~25,000 people that is connected to Manhattan by rail. In the past few years we have seen several hundred rental units be constructed in the center of the town. This is not atypical. Similar buildings have been going up throughout the region for years (although most affordable options are connected by bus rather than by train).
I have to agree with GP's conclusion that California's problems primarily stem from its tax system—which is objectively ridiculous. If every time you move houses your tax rate resets and suddenly you are paying 10x (or more) in taxes than you did previously, why would you ever sell?
In the NYC metro area, most of the people who in California would be suburban NIMBY types live and work in high-property-tax areas in relatively big homes while they raise their kids and send them to public school (which are well-funded by high property taxes). It is very common that when their kids go to college they sell their homes and move to smaller places (or to, say, Florida). They are incentivized to do this because doing so will lower their tax bill. As a result, the real estate market is very liquid, with most homes turning over every 15 to 30 years.
In California the tax system works in the opposite manner, by disincentivizing sales. Even inherited property isn't sold, because doing so would result in a reduction in the net cash flow that the property can yield. Isn't it the case that most heirs typically sell property they inherit, in order to have access to liquid funds that they can use in a manner that is more consistent with their own personal needs and preferences? Not in California! In California, if you inherit a house, suddenly you are a landlord.
None of this is to say that there isn't political resistance to higher-density housing in the northeast. There certainly is. However, the way that this resistance is typically mobilized is through the use of zoning restrictions. Zoning restrictions can be amended—and have been amended—as the need for housing has grown.
If people are not willing to sell their properties—if the real estate market is not liquid enough in a certain area—then new development will not occur, regardless as to whether or not zoning ordinances are changed. In fact, the primary advocates for zoning changes are often developers who want to build specific projects. If there are enough properties for sale in an area to attract the interest of developers (and capital that legacy owners may not have access to), then it is more likely that there will be effective advocacy on a local level to amend zoning rules that will result in a more profitable use of those properties.
If no one is selling, however, and if no one is buying, then no one has any interest in changing anything with regards to how the land is used.
