You misunderstand both my premise and basic economics.
I would recommend reading the original Wealth of Nations by Adam Smith, which forms the basis of modern capitalism.
https://www.gutenberg.org/ebooks/3300
It's clear, analytical, and mostly correct.
Chapter XI, The Rent of Land, is pretty quaint at this point, but gives a compelling counterpoint to your argument. It begins:
"Rent, considered as the price paid for the use of land, is naturally the highest which the tenant can afford to pay in the actual circumstances of the land. In adjusting the terms of the lease, the landlord endeavours to leave him no greater share of the produce than what is sufficient to keep up the stock from which he furnishes the seed, pays the labour, and purchases and maintains the cattle and other instruments of husbandry, together with the ordinary profits of farming stock in the neighbourhood. This is evidently the smallest share with which the tenant can content himself, without being a loser, and the landlord seldom means to leave him any more."
The basic analysis of the chapter can be translated from 1780-era industries into 2025-era industries, and explains much of how housing markets work.
If you would like contemporary data, I would recommend looking at the impact on the price of housing of European cities which offered nationalized below-market housing.
A central fallacy in most of the libertarian space stems from the difference between industries which are not zero-sum (e.g. manufacturing, software, writing, etc.), and rent-collecting ones (e.g. literal rent, much of finance, mining, etc.). Here, I use "rent" as economics jargon, not common meaning. You can look it up.
Being used to operating in domains like software -- which has literally zero marginal cost -- there is a natural tendency to want to extrapolate the same dynamics to other industries.
However, economics works out differently in industries like that. For the most part, if there is a finite amount of stuff, it makes sense to divide it fairly to avoid dynamics like that. If you're producing stuff, it makes sense to divide it according to how much you contribute.