> Land is expensive due to artificial scarcity created wholly by regulation.
This is a bit of a strawman. I suggest you broaden your perspective and don't only rely on narrow US anecdotes in order to try to explain global phenomena.
I live in Asia where there are essentially, especially from a Western perspective, zero regulations. (I've never seen a house with a smoke detector, for instance.) And land is still expensive. In a country where the per-capita GDP is under $3,000 a year, the houses in my neighborhood still cost over $500,000 and most of that is the value of land (parts & labor for building a house of that size are only about $150,000). And the city I live in has a population over 13,000,000.
"Building up" doesn't happen magically. It takes investors willing to put up tens to hundreds of millions of dollars for an uncertain payoff many years in the future. That kind capital simply isn't trivially available here.
The road to my house is wide enough for a single car -- and it is in quite poor condition. The roads flood every year (up to about half a meter) during the monsoon and "flooding" means sewers are backed up so it isn't pristine water we're talking about.
All of that infrastructure needs to be improved to increase density by "building up". In a developing country, those things are in the condition they are because the local city has an insufficient tax base to fix things in the short term. Again, it doesn't happen magically, easily, or instantly.
What's more, there are constraints to "build up". Every house in my area is already four stories tall. Because of the high water table, there's no such things as "foundations", so every house is built on top of dozens of steel piles driven 20 meters into the ground. Construction of new houses regularly causes damage to adjacent houses, due to the unstable land. Construction here is primarily of brick, which has height limits due to weight. You can use other materials but then you have additional costs of needing to import materials and not having workers with experience in it.
Sure, it is possible to take all those four story houses and turn them into eight story houses. It just takes an extra level of complexity of architecture and construction.