Housing policies, and zoning laws in particular, are a great example of major social policies that probably have large impacts on health, but are rarely evaluated as health policies. I like the numerous mechanisms you note- many of these would presumably be related to segregation in particular.
The challenge, as you note, is developing a rigorous design to demonstrate which aspects of policy we might change to improve health. A case study describing the differences between two cities can be compelling to motivate ideas and suggest hypotheses, but it will rarely be convincing about the impact of specific, modifiable policies, for exactly the reason you note: there may be many other reasons that, Chicago differs from, say, "WiseZoningVille", that are not necessarily due to zoning practices. This is partly so difficult because we are not just asking about the effects of one person's house, but about the effects of a whole neighborhood, or the policies prevailing in a whole city. Thus, the effective unit of analysis is a city or a metro area, and it is difficult to have enough data. Often the most rigorous designs rely on changes in exposure within a unit of analysis (e.g., someone goes from unexposed to exposed, does their outcome value change in tandem?). In this case, we would need cities that changed their zoning laws, and to evaluate the health of their residents before and after those changes. But since the zoning laws may take years or decades to impact health, it is really tough to build a convincing case.
Some of the most convincing examples rely on natural experiments, e.g., the city build a new transport and this meant two neighborhoods previously isolated were now connected - what did that do to the health of residents? But few studies have really explored this type of natural experiment carefully.
Maria