I think the thing that would help the most would be to get rid of single family only zoning. That should result in a lot more, higher density housing being built. However, that’s not going to bring down the price of single family homes. In fact, it would probably make them more expensive. Maybe not everyone would think that’s such a good thing, but it’s absolutely necessary if we want to reduce car dependency.
But I think the reason there isn’t space for everyone in many cities is because a large percentage, or even a majority of the land in many cities is zoned for single family only, even very near downtown areas. I think parking requirements have a lot to do with it as well, since they result in parking lots being built where condos, or other multifamily housing could be built. Theoretically if you get rid of single family only zoning and the parking requirements, more housing units could be built, even larger units, increasing their supply relative to the demand, thus bringing down the per unit price.
But maybe that theory is flawed. Maybe the problem goes deeper than zoning and parking requirements. A lot of these real estate developments are investments, and investors have an incentive to not build so much housing that the per unit price goes down significantly. Some people might argue that developers and investors could make up for lower per unit prices in volume, but that’s only true if they are large enough and have capital resources to produce at that higher volume, which might be fine for very large developers and investment companies, but not for smaller ones. Plus, large or small, why try to make money selling or renting more units at a lower per unit price when you can make the same amount of money selling or renting fewer units at a higher per unit price?