Public services can be exempt from economic forces if a society deems them worth the cost. Generally in most first world nations you aren't denied life saving treatment on a cost benefit analysis.

In the same vein, it seems like its almost necessary that governments be leading the density charge in building. There should always be a public housing option everywhere, and it shouldn't be a default ghetto. Japan does an extremely good job providing a baseline amount of public investment in dense urban housing that helps regulate the unit supply the private market is otherwise managing.