Earlier quoted context omitted.
I'm confused by this objection, if you draw a stereotypical supply and demand curve, you can see how prices settle to an equilibrium point. Of course reality has more complications, but I think your objection is 95% answered by a supply and demand curve. You keep building houses when it is profitable. You stop when it is not. This naturally keeps everything in balance.
Free markets for housing are likely to settle into an "optimum" where some percentage of people cannot afford housing at all, because while construction/rental of housing for them would net a return, it's not worth the opportunity cost. Plus you should not wait for the market to respond to a lack of housing: people will be homeless in the meantime. Supply/demand is mostly reactive, because building for anticipated fu…
I don’t dispute that there are levels of affordability that are bad enough that they start to lead to various forms of homelessness, but it doesn’t seem to me like a fundamental rule that, if some people can’t afford to live alone in a large amount of housing, they also can’t afford to live with roommates sharing a smaller amount of housing, and that the right level of housing prices should also price some people out of those arrangements (ie it demands a pretty high level of inequality if you assume that the market allows typical people to afford to live alone and that sharing can typically reduce per-person rents by half or more)