Unfortunately it is genuinely a complex problem. It is true that in general adding more housing lowers prices, but in detail the exact opposite is often true. F

Unfortunately it is genuinely a complex problem. It is true that in general adding more housing lowers prices, but in detail the exact opposite is often true. For one, adding housing can lead to more demand for services (eg schools) which in turn makes a location more desirable which makes more people come which makes housing prices go up. The densest cities in the USA are also some of the most expensive for housing. On the other hand, decreasing demand (eg people leaving) doesn't always fix socioeconomic problems either - sometimes, once people start leaving, more people leave until you end up with an empty husk of a city eg Detroit at one point. People need services and people also want to be around other people like them. This causes feedback loops, making the nexus of problems related to housing truly and inescapably complex.