You need to separate land value and house value.

When regulations are reduced to allow more density, the value of the land goes up because its productivity increases. The land can do more now, e.g. hold 10 apartments vs 1 house. The same land generates more rent so developers are willing to pay more for that land.

Meanwhile, the value of housing units goes down due to increased competition among sellers/landlords.

Consider two zoning changes.

1) You are a homeowner and more units are allowed on your parcel, e.g. single-family -> duplex. That increases your land value.

2) You are a homeowner and there is more density around you, but not on your parcel, e.g. apartments are allowed nearby but not on your street. Your land value does not increase. Your home value decreases due to increased competition. (Of course, there may be long term effects like the increased density actually leading to economic windfalls in the area, increasing its desirability, and then increasing your home value.)

Isn't the parent article basically evidence of this? Housing supply grew, and prices fell.

it's not that density per se drives down existing costs, but density almost always brings more housing stock to the market (unless they are simultanously tearing down housing elsewhere) and housing stock drives down the cost of housing, which is the point of the original article.

So if we take it as an assumption that density increases housing stock, there is lots of evidence that density drives down prices of existing land/home values.

in fact, density increases the value, because the original plot can now be resold at a higher price for a hi-rise.