The fact that the few dense cities in the US where you don't need to drive everywhere are ridiculously expensive would indicate there's more demand for these kinds of places than we're supplying.
Likewise, even the most expensive cities still have mansions in the middle of micro-apartments. If these cities really were valued for their density, the mansions would either be gone or would be cheaper than the surrounding dense dwellings.
Does density imply micro-apartments? What's a micro-apartment? What's considered dense development?
Are we looking at this through a macroeconomic model or a microeconomic model? If microeconomic, have we accounted for everything that confounds consumer choice and consumer demand?
Given strict regulations on land use—the status quo today—is it reasonable to assume that mansions or villas within the city limits will be granted permits for denser development, whether that means interior renovations to convert them into multi-unit dwellings or razing the building and starting anew?
The analyses so far plainly seem too simple.
The implication you've stated, which is itself a more informal restatement of what originally started this thread, hinges on whether the conclusion "we don't have enough high density accomodations (sic)" is true. The premise "prices are too high" has no bearing on the proposition's reasoning. (At least, if you take it to be true, which I feel is the case for most people.)
Is the competitiveness of the housing market overall not an indication that we lack accommodations, let alone high-density ones?
This all said, if it actually were a converse error, taking "prices are too high" as the consequent means that the premise "we don't have enough high density accomodations (sic)" has no bearing, which seems off because, surely, there's some connection between the supply-demand model and price.
My doubt is based on two facts: rich people don't go for the dense living even in these areas and nobody is building residential high raises in the cheap areas, which would have been a huge missed opportunity if there had been a genuine demand for the dense living conditions.
I think the thing that people on HN don't think about or make explicit in this kind of argumentation is that there are certain amenities that folks prefer to have nearby, and they kind of miss the neighborhood for the houses, as it were.
It isn't necessarily the density itself driving the demand; it's often the reasonableness of, e.g., being able to send a child off to the post office or supermarket to run an errand. Therein lies the rub: Density tends to be a sufficient condition for enabling that.
That said, beyond a certain wealth stratum, none of this really winds up applying anyway, so it's less useful to talk about those folks would do.
Which is exactly what I said:
https://news.ycombinator.com/item?id=31891305
Saying "Well if people love their density so much, why don't rich people cram themselves in the tightest possible density" is a strawman.