I tend to think that housing shortages are more a result of inequality than a cause of it. The large disparities in wealth result in a situation where a disproportionate amount of land is controlled by a relatively small number of people. Those landowners may be fine with owning "trophy" properties that do not produce any income stream but take up a lot of land that could be used for housing a lot more people. Also in some areas an increasing amount of "housing" is not used as housing but rented out as AirBnBs.
Simply allowing landowners to build more housing on their existing land, and thus increase the value of that land even more, will exacerbate this inequality. Again and again I see unaffordable housing built because the developers complain that they cannot make a profit otherwise. I am suspicious of "solutions" to housing that amount to "remove regulations to allow rich people to build in a way that increases their wealth". Instead of allowing greater density, we need to require greater density, i.e., go to people who currently own a lot of land saying "Either you build a lot of housing on this land, even if it causes you to lose money, or you forfeit the land."
The housing shortage should be reduced by taking from those who already have a lot, not giving more to them.
My favourite example of this in my neighborhood is an apartment block of only studios, which would be illegal to build today, as the law was updated to prevent ridiculously small apartments (18m2) from being built.
It is, of course, half empty, but it doesn't matter. Those who bought those units never intended to live there anyway. To them it's just digital currency where proof of work is a physical object.
People advocating for "just" building more housing have no idea who buys most of the properties.
Simply allowing landowners to build more housing on their existing land, and thus increase the value of that land even more, will exacerbate this inequality. Again and again I see unaffordable housing built because the developers complain that they cannot make a profit otherwise. I am suspicious of "solutions" to housing that amount to "remove regulations to allow rich people to build in a way that increases their wealth". Instead of allowing greater density, we need to require greater density, i.e., go to people who currently own a lot of land saying "Either you build a lot of housing on this land, even if it causes you to lose money, or you forfeit the land."
The housing shortage should be reduced by taking from those who already have a lot, not giving more to them.