The other way of looking at this is imputed rent, the amount of money that somebody would be willing to pay to rent out their own home. Well, in theory it would be that amount. In high-demand areas, homeowners' actual imputed rent is higher than they would be willing to pay, because the act of buying property and paying low taxes let's then live in their place for far less than somebody else would pay for the same privilege. Which is how opportunity get hoarded, and how rentiers take over local governance structures.
I'm not sure that's not what happens regardless, except for the two things preventing it right now.
The first is the existing property tax. If increasing the size of the building on your property increases your property tax, you have to recover that in addition to the construction cost from rents or it isn't worth it.
The second is, of course, zoning. Even if it would be cost effective to build a 20 story building on your lot, you can't do it if it's prohibited by law. If you can't build upwards then you have to build outwards, which requires land, which transfers the scarcity of land into a scarcity of housing and prevents rents from falling to the construction cost.
And you need to fix that for LVT to do what you want it to do. Otherwise the artificial housing scarcity persists and the money just goes to the government instead of the landlord, and gives the government a direct rather than indirect incentive to maintain (or increase) housing scarcity through restrictive zoning.
For example, instead of a cap on a neighborhood of three stories, the cap could be 33% more than the tallest structure in the adjacent two blocks. Or 50% more than the median height of the adjacent two blocks. Or maybe the max or min of those two values. The key would be to have it be not subject to delayed political approval, but rather responsive to what's going on in the neighborhood.
The other thing that's necessary is something like the Greek polikatikia model where the owner of a house can easily have a larger structure built and get a new place in the larger structure:
https://www.bloomberg.com/news/features/2020-07-15/the-desig...
I was just thinking about this a little more and I think this is actually quite bad.
Because rents falling to construction costs is relativistic. Suppose it costs a given amount to build a 20 story building and you can recover at least that much in net present value from it in rent. Then you're going to do it if it's permitted and you have an empty lot. But not if you have an existing 10 story building. Then it would have to generate double the construction cost in rents, because you're getting half that amount of rent from the status quo.
Which means that to minimize that inefficiency, you don't want to be replacing 10 story buildings with 20 story buildings. What you want is to be replacing 4 story buildings with 20 story buildings. Because then you only have to beat the construction cost by 20%. Which doesn't work well if you have to wait until the median building is 10 stories tall before you can build a 20 story building.
But it's not completely wrong if you use different numbers. Say, have three classes of zoning. One allows buildings up to 4 stories, the next buildings up to 20 stories, the last unlimited. You automatically transition from the first to the second when the median building height reaches 3 stories, and from the second to the third when it reaches 6 stories.
The part I believe more strongly in is decoupling the political process from geographic-specific height restrictions. We need to have a political process to derive the general rules for automatically allowing increased density, but any specific site should not have special rules except perhaps for geographic or environmental reasons, and that should be decided at the same time as the general zoning rules.
The real error in California and most of the US has been to downzone everything to current structure levels, then only allow additional building through a political process of granting exceptions. This leads to massive corruption (see LA's city council, for example), as well as increased land speculation.