> Meanwhile, the cost to the city in terms of infrastructure (pipes, roads, drainage, etc) is much lower than the houses in the subdivision down the road
The costs in terms of lots of services that aren't physical infrastructure scales with population, though, and for some services (or for adverse impacts that services don't fully mitigate) is also higher, rather than lower, for the same population when density is higher; e.g., crime rates per capita tend to go up with population density.
The base of the land value tax is the value of the land though. If the land is in the middle of a high population density area then the land is worth more and it generates more tax revenue.
The difference between this and property tax is that if you have a 12 story building on one piece of land and a 2 story building on the adjacent one, otherwise identical piece of land, they both pay the same tax, giving the second property owner more incentive to build.
You only do this in the places where you want everything to become skyscrapers. There is no real need for it in Des Monies or other places that already have reasonable housing costs.
The costs in terms of lots of services that aren't physical infrastructure scales with population, though, and for some services (or for adverse impacts that services don't fully mitigate) is also higher, rather than lower, for the same population when density is higher; e.g., crime rates per capita tend to go up with population density.