> On the social side: the gamble is that social growth will outpace the increased economic pressure. Meaning, you need the new vertical growth to create opportunities faster than it increases prices further in the area. A land tax alone wouldn't pull people out of poverty, create affordable housing, or open up public school. Those are all just potential avenues for the city to develop, not guarantees.
There are a lot of ill defined and bizarre things here. What is "economic pressure"? I have never heard such a term before. Why would there be "price increases" (inflation)? I have never heard anyone serious posit a link between density and inflation. It's the exact opposite because economics of scale and scope can deliver services more efficiently. Why shouldn't a land tax contribute towards "affordable housing" when the economic logic predicts it will have a deflationary impact on housing costs? Why do you think I'm saying that a land tax will "open up [new] public schools"? I said there would be a change in incentives away from excluding poor people from your local school catchment area, which has historically driven local resistance to upzoning. Honestly, it sounds like you should read up on basic economics before you form these opinions. The subject matter is primarily economics and such basic knowledge is a prerequisite to understanding the rationale behind one tax or another.
> The more you build up the more steel, concrete, glass, energy, etc is needed.
No, this is forgetting that you have the same number of people in either scenario. It takes more resources to build 1000 single detached homes (and associated roads, train stations, shops etc) than 10 apartment buildings with 100 homes (with less roads, less train stations than the former scenario).