This is counterintuitive because the cost of producing anything goes down, so you'd assume cost of living goes down. Unfortunately all production (and consumption) requires land, and as productivity rises, so does the cost of land. This isn't because the inputs into land get more expensive. It's for no other reason than that landowners are able to charge more because the land is able to produce more.
To point out the obvious: a landowner in a low productivity region does just the same as one in a high productivity region, which is to say nothing at all.
The land would be there available for use even if no one at all owned it.
This cost gets baked into every single input into every single good and service. The reason a meal is so expensive in New York City as compared to Oklahoma City isn't shipping costs. It's the rent of the restaurant and then the higher wages needed to pay everyone in the restaurant due to their elevated rent needs.
Rent rises (and falls, but more slowly) to exactly the level required to keep some portion of people in poverty and near-poverty, no matter how productive the local area is.