Unfortunately, there's a lot of people -- especially further left -- who fight this kind of reasoning. They insist that the housing market is different, and that just building more private housing won't help.

No amount of evidence will convince these people, because they already made up their mind ahead of time: their ideology says the market can't help, so the market can't help, period. Any evidence to the contrary is a plot by billionaires or something.

Their core argument is that we could increase supply but choose not to, and that we should be maximizing supply (as an ethical and moral mandate, but that is not a tenant of capitalism really) because housing is an essential thing like food and water. FWIW we don't maximize food/water production either for various reasons, which would also drive food/water prices down.

Maximizing supply can mean other things than building like taxing unoccupied homes by large amounts making them unpalatable to own as a second (or higher) home, thus putting them back on the market. However these aren't all good because obviously our economy deals with more effects than just simple supply and demand, like maximizing the amount of loans given to people wanting housing regardless of the ability to repay is known to be a bad idea.

If you throttle the supply you can clearly control the price and the people you're talking about believe there is a concerted effort to control that supply. This can happen directly (choosing not to build as soon as land is available to build on) or indirectly (e.g. politics, mass media influencing people to vote to not increase supply).

What people generally hate is production of essentials not being maximized which would give us the actual lowest price, and maybe we as a society should be maximizing that supply to arrive at the lowest cost for a given house with given features.

And then the rebuttal to that is usually "tough shit lol" which is why people coming out with simple supply and demand replies are generally seen as derisive.

The populists on the right share a similar view, but mostly blame immigration.

There's a lot of talking past each other on this issue. Sure there's probably clueless people out there, but a lot of left wing housing activists that are skeptical of free market housing liberalization understand very well economics and the benefits of housing supply, but are concerned about the time horizons involved and concrete near term impacts on low income residents.

It is of overall net benefit over the long term to raze a small three story walkup apartment and build something denser, overall increasing the amount of housing.

However, in the short term it's immediately quite (sometimes existentially) bad for affordability if existing affordable housing is destroyed and replaced by brand new (and thus inherently luxury) housing.

So accordingly we naturally see low income housing activists push back against some redevelopment and ask why development is not occurring in wealthy single family home areas where the amount of people impacted is less and class those that are not remarkably negatively impacted.

Personally I think the data shows that in general it is still really beneficial to build out as much housing as possible and avoid the negative impacts of a shortage, but I do think there are people validly pointing at a real problem of displacement.