This kind of anti-logic usually goes along with arguments like "well, they keep building lots of units and prices haven't gone down, so obviously it's useless to do anything but enact rent control for current residents and give the middle finger to anyone else who ever wants to live in that place", while ignoring that prices can't go down until we catch up on the literally decades of underbuilding in most US metro areas.

If living in a denser place turns out to be more desirable due to better jobs and/or amenities, the demand effect can be so strong that it more than offsets the increased supply. But that's actually a very good thing; it means that dense housing is unlocking even more value than you might have expected it to.

Dense housing creates highly walk-able cities with extremely good public transportation. Furthermore, high density foot traffic creates improved economies of scale for businesses. Economies of scale might shift society to one where you don't need to cook at home because good inexpensive food is everywhere. Businesses themselves benefit from high concentrations of skilled workers in more condensed areas. The total cost of commuting for society diminishes. Public works also benefit because more people can benefit from every dollar spent. Dense living lets people take advantage of the economies of scale of the businesses and infrastructure around them.

The end result of dense housing is a highly desirable place to live, in other words, increased demand for housing, locally.

This can be seen in housing prices in NYC, Taipei, Seoul, Tokyo, Hong Kong, Singapore, etc.

So it is not dense housing that makes housing costs drop, it is dense housing built in excess of demand... But incumbent property owners will resist that tooth and nail because if production of housing can satisfy demand, their capital investments (and very often sole vehicle of retirement income) will decrease in value. When a person's wealth decreases, they desire political change. So housing policy that results in lower housing costs is extremely unpopular among those with power (education, money, time, etc.).

Devil's advocate: induced demand. Density increases interactions which are the economic point of cities, and why cities are wealthier than suburbs/rural areas (when suburbs/rural areas aren't juiced by subsidies and loans). Wealthier cities attract migration, migration increases demand for units.

That said, my personal belief is that prices are completely decoupled from demand and are more reflective of a desperation to keep them high for... other reasons.

> How does building dense housing lead to higher housing costs? That seems unintuitive to me.

By creating a denser unit, you're forcing (via economic forces) more people to move closer to denser areas. This in turn makes these areas more attractive for employers, making it easier to do business. This in turn makes dense areas more attractive for employees, so they are willing to pay more to live closer to dense areas.

Result: density increases, and prices rise along with it.

And an additional toxic component: the population is basically not growing anymore. It's nearly a zero-sum game now, so each new dense unit means one more dilapidated house in Kansas as its occupants had to move to find a job.

Here's a great post from a person living in Tokyo: https://news.ycombinator.com/item?id=39331618