I doubt zoning has any real effect. Henry George realized in the 19th century that if you increase the money supply most of that money goes into driving up the cost of real estate. And the government has been printing money like crazy for decades now.
Where I live there aren't too many restrictions on housing, but a developer friend tells me he can barely make a profit at current prices because of 1) the cost of the land and 2) modern building codes make housing a lot more expensive. You can have cheaper houses if you're willing to give up things like the insulation that forces builders to use 2x6s instead of 2x4s for exterior framing.
That NIMBY stuff is mostly a problem for pricing if you want to live in a big city.
