The only one who the cost of materials matters to is the builder. If it costs them more to build than they can sell it for (within whatever % profit margin they want), then they simply won’t build it.
Which, as a catch-all condition, is next to useless to examing why the price of something is what it is.
The question then moves to the next turtle: why are people willing to pay X for a house in area Y.
>The cost of building is not relevant in any way to that.
Well, that's not true. In a place were land is plentiful and cheap, the price to get a house is dominated by the cost of building. Doesn't matter if there's an existing house that someone is willing to pay 100 for it. If people can trivially buy land and build for 20, that would be the cost to own a house in the area (note: a house, not THAT particular house).
Definitely true, just look at home prices in the south and midwest where there is plenty of land [0].
[0]: https://www.supermoney.com/inflation-adjusted-home-prices/
It's not about there being cheap land in the state in general, it's about being cheap land where people want to live.
Or, inversely, sure, home prices in the south and midwest might be high in expensive areas (e.g. major city), but they're much lower where land is cheap.
I may be happy to buy a house for anything less than 200k but if all houses are selling for 100k, then that (or something like it) will be the amount I am actually willing to pay.
If construction costs rise and now builders are only selling houses for 150k, I will now be willing to pay that price.