Generally the obstacles to cheaper housing are political. For a building of a given footprint and height its normal for people to show up at planning meetings

Generally the obstacles to cheaper housing are political. For a building of a given footprint and height its normal for people to show up at planning meetings asking if they could maybe have fewer, larger apartments than they intended so that the new building causes less traffic. We have the technology to build buildings pretty high and the capital cost to do so is a small fraction of the reason housing prices are so high in major cities. I'm open to the idea that at the margin a little less safety for a little smaller cost might be a good or bad tradeoff but this isn't a decisive battle.