I wouldn't say regulation is the same as geography. For one, it's self-imposed. Second, it costs a lot less to build up than to build out. Note that Chicago has a very densely built core, even though it has no real barriers to sprawl to the north, west, or south. That's the result of (lack of) regulation plus good urban planning.
This is another fair point, but consider the land is massively more expensive. The dynamic is relative scarcity and bargaing power. The more scarcity, the more the economics look like monopoly on the underlying asset. At that stage, the cost of building out is sort of second order.
The other examples, such as London, Geneva, and SF have a combination of massive wealth (in both flow and assets stocks) combined with constraints on the ability to build due to geography/history/etc.
I agree some of ths (like greenbelt and listed buildings in london) is by way of law, but most rent control follows from the combination of scarcity/wealt co-existing prior to legislative means to "provide access". In other words, those laws follow the sort of self-evident understanding that if left unchecked, the dynamic of quasi-monopoly rents being extracted from the real-estate market will lead to all kinds of bad things down the road (social tension, and its variants, primarily).
The other counter-example perhaps to chicago or LA is tokyo (which is pretty spread out). But again, there is a social dynamic of scarcity (JP is very hiercarchial/aristocratic society) and Tokyo is both the financial/business and political capital of JP. Even in the 80's the somewhat absurd cost/ft did not hinder people from needing to be in Tokyo for their careers. Rather, the all just gave up having more than 1 kid to afford the astronomical cost of living. A generation later, the population growth is almost not feasible given the entrnched cost structure of real-estate and the need for the few young (workers) to support the many old (retired).
After the 3/11 quake, I did a lot of thinking about what would happen if Tokyo became unlivable .. It, basically, freaked me out. There's a lot of Japan stuck in just one spot..
Right, I overstated the equivalency, I should've said something like "plays a similar role."
But, does it still cost less to build up than out, in a city with nearby land for the cheap, taking into account that you have to build your upward development in a way to be competitive with 2000+ square foot houses and yards? There's definitely some upwards building being done in the cores of the cities in Texas, but a whole lot more building out. Overcoming the lack of urban planning in the past is where it would get pricey, and need a lot of buy-in.
Would you say the relative cheapness of housing in a lot of Chicago compared to more mountain- or water-locked cities has more to do with the planning/regulatory environment or with the open geography on the non-lake sides?
I guess my point is there is more to it than just geography. Clearly the availability of cheap land lowers the price of housing, but Chicago is more densely built than say Seattle or Portland while also being cheaper. The downtown core is comparably dense to San Francisco but much cheaper.