That relationship doesn't hold in ski resort areas. Wealthy people have increasingly bought up vacation homes even as the population remains flat. Those vacation homes are vacant much of the year. There are usually geographic and infrastructure constraints which make it impossible to build significant amounts of new housing within practical commuting distance. So long time local residents are effectively being forced out.
I have little sympathy for people that are "forced" to sell their homes for a large capital gain. They can move to where it's cheap and live large. Maybe my perspective as an immigrant is unusual, but I'm a big fan of the freedom to migrate. That includes the freedom to buy housing at market price.
Then it's even easier to move. If the polity doesn't want to zone for more housing, they've chosen to expel people who can't pay more than $X for rent. They'll feel the pain when there's no one around to make their coffee anymore.
There's no such thing as unlimited demand for luxury housing. Build enough and the rent will fall for the existing housing stock.
Moving requires finding a home somewhere that they can afford. The fact that they’ve been subjected to rising rents rather than a financial windfall like nearby homeowners… makes that far more difficult for them
They could have bought. Instead they took advantage of the optionality afforded to a renter that can up stakes and move at will, without being tied to a mortgage.
If they couldn’t afford to buy then they got to take advantage of a locale they desired at a lower price, another benefit of renting.
(While it would be nice if anyone could live — and own — anywhere they like without worrying about price or competing demand from the billions of other humans around, that’s so far away from reality it’s not worth discussing.)