At some point your market solutions will have to wrestle with the problem of "how do you get people to give up the stuff they want and the expectations they have", like lawns, quiet neighborhoods, not being around poor people, etc. And the answer is inevitably some variant of "with the force of law", but with an eye towards making sure the current socio-economic stratification is maintained to some arbitrary extent because the currently wealthy deserve to maintain their wealth more than the needy deserve to have aid, any other outcome would be "unfair".
Also it's not like Hong Kong, a shining beacon of the merits of market balances for housing, isn't facing its own unique humanitarian crisis:
"Yes the cage apartments are bad but it's better than living on the streets, the market works!"