I believe you have used circular reasoning here. The price is ultimately governed by supply and demand. They are expensive because more people demand them than the supply available for sale. There are many reasons why demand can exceed supply, like development restrictions, difficult building environments.
That's no different in a pretty rural area or in a place like the bay area. The extremely pretty and expensive rural areas (think luxury ski towns) control housing development even more strictly than expensive cities. The bottom line is desirability, which manifests as demand.
And, if you're paying $1M+ for a house in the rural plains, it's probably far bigger than the typical house, because the land is very cheap.
You may have a piece of property that only one person in the world wants to live on, but if you get a single buyer willing to give you a million bucks, you have a million dollar property.
Meanwhile, 100 people might want to live in a particular property in a ghetto, but none of them have a million dollars to bid on it. The price will only raise to the maximum amount that the buying pool can afford. More demand doesn't result in higher prices, it results in homelessness and/or people moving to alternate markets.
My point is that $1.5m prices are not a signal that a ton of people want to live in a particular place. It's a signal that people who can obtain $1.5 million dollar loans want to purchase there, and that the demand satisfies the motivated supply. That's it.
I don't know where you are referring to but there is reams of historical data that demonstrates that more demand without an increase in supply leads to all 3 of those.
> My point is that $1.5m prices are not a signal that a ton of people want to live in a particular place.
Yes, and $1.5M in isolation is a meaningless number and not a signal of anything at all without describing what exactly it buys you.
What does signal desirability is the trend line in property prices in a given area and the relative price of equivalent properties in different areas.
These houses and the areas they occupy (i.e Beverly Hills, Park Ave ) are an extreme edge case, and don't exist in the same housing market as normal houses.
Above a certain very high price percentile, there are always very few buyers and sellers, and they are all paying a high premium for things like high physical security.