Look at Japan. They have much less restrictive zoning so.....housing is WAY CHEAPER. I'm not sure why you think that fixing a fairly obvious problem won't help anything.
Japan has a declining population, housing is cheaper in places with declining populations. Additionally, housing in Japan is often much lower quality than it is in the US, where they use electric heaters and various other plug in amenities rather than ones that are built as a part of the unit.
Zoning reform will at best only make it cheaper for high earning single people and small families to find housing in dense cities 30 years after a reform is implemented. Where, the only real solution is figuring out a way that would allow us to build dense urban multifamily buildings at the same cost per square foot as single family homes.