Denser areas are cheaper per housing unit. Building an apartment building might cost 10x as much as building a house, but it can probably house more than 20x the households.
LVT in an urban/suburban area incentivizes building more housing units per surface area. And a power law formula LVT would especially align incentives, as land that is worth more has even more incentive to be developed.
That doesn't make a lot of sense. That's just increasing scarcity of lands. What that example means is that land that the apartment is built has minimum 20x more value over each individual units.
It would make sense if your argument is that $1m/unit, 50-150 floors tall, 500 units total apartments intended exclusively for young and current childless dual income investment bankers households, seen everywhere in developed cities such as NYC or Shanghai or Singapore or likes, is exactly the intention of LVT and desired steady state of land price inflation control, but I assume it's not?
Now sure, if everything else is equal then yes it is true. Building a small apartment building on the same land as a single house will result in more units than the cost multiplier of the build, so as you say, they'll be cheaper.
But everything else is never equal. It only makes sense to do such increased density in an area that is becoming more and more expensive and the delta increased density will make the area even more expensive.
NYC is the densest area in the US, and is not exactly known for the cheaper per-unit housing costs.
LVT in an urban/suburban area incentivizes building more housing units per surface area. And a power law formula LVT would especially align incentives, as land that is worth more has even more incentive to be developed.