There is "rent seeking" (a microeconomics term for a market inefficiency using politics for wealth creation instead of true wealth creation) by having zoning laws which keep land use density artificially reduced as well as over-using "historic landmark" laws. The zoning restrictions on land use and the overuse of historic landmark laws effectively make very wealthy landlords and other landowners wealthier still at the cost to others. See writings of Harvard economist Edward Glaeser for more details.

This is something that can be fixed by reducing the market inefficiency of "rent seeking" through state law which overrides the desires of wealthy landowners at the city level.

Zoning laws can pose a lot of restrictions on where those houses can be built, so it depends heavily on the city. Basic physical obstructions and topology also play a role. Adding more homes onto far out suburbs isn't going to do much to massage the problem of unaffordable housing near downtown office districts if it means that homeowners have to commute an untenable distance.

Which makes substantial profits for the home builders but very little in the way of more affordable housing.

The price of a barrel of oil is determined by supply and demand. As the price goes up, more production is brought online which is now economically feasible. So at $100/barrel you've got the Canadian tar sands projects which make oil for something like $80 a barrel worth of cost so the company can make $20 a barrel.

But there are still tons of wells out in west Texas that are producing oil for $20 a barrel in cost. The people that own those wells are making $80 a barrel in profits.

If housing prices are high home builders might be able to build less expensive houses but they have no incentive to. They can sell the houses they build at market rather than below market prices. It might increase the supply but that doesn't necessarily translate into reduced prices in any kind of a reasonable timeframe.

The availability of usable land is fixed. There's a limited amount of single-family homes you can build in a given area.

In the UK when house prices go up people tend to build more houses at the top end of the market where there's the most profit. No one builds cheap houses that people on a single income could afford. I don't know if the US is similar.