You asked this question: "Why wouldn't businesses just relocate to cheap housing areas?"
That's a legit question, and one I don't think has been adequately answered, probably part of the answer is that they do.
Answer: Because if a city is cheap it's likely in decline. Just like a business has issues if it stops growing, so does a city. And the other cheap areas are going to be "wherethehellarethepeople, USA".
Not necessarily. The paper doesn't claim that as far as I can tell.
Success breeds success. The reason tech goes nuts in places like Seattle, SF, DC, etc. is because there are other tech industry employers there and it results in workers and companies both being attracted to the area, building a Katamari ball of talent and employers utilizing that talent. If you set up shop in a lesser market you end up at a competitive disadvantage when attracting and recruiting talent.
This views success as a static phenomenon that doesn't change between cities. If you have success, then you have more success, thus higher housing prices and regulation in perpetuity.
The NIMBY issue we see in NYC, SF, and literally every other city is that property owners don't want to share. They see their taxes going up, their homevalues going up, and they want to keep the ball rolling and keep the "undesirables" out. And so they artificially restrict development to further buttress their position.
The paper uses Atlanta as an example. Lets note Atlanta
is not rural.
The Atlanta market is a canonical example of the second type in which supply is highly elastic and demand always is strong enough keep prices at MPPC. This is the textbook example also depicted in Figure 3 in which demand intersects supply on its horizontal part. If demand grows by a little or a lot, a sufficient number of units is delivered so that developers cannot earn above normal profits. Figure 5 shows what happened to permitting activity in this market. New supply is highly volatile. Permitting intensity was running at 3% of market size in 1985, but then fell 50% by 1991, as the local economy declined. This was followed by a long building boom, as annual new supply more than doubled to nearly 4.5% of market size in 2005. The onset of the global financial crisis then saw permitting plummet to below 0.5% of market size by 2009, and it has only recently started to increase again in the Atlanta area. Amidst all this variation in new supply, the median owner's price-to-cost ratio never varies much from 1. This is consistent with the supply of housing being highly elastic and demand fluctuating about a horizontal supply schedule.
That population growth has occurred during the time frame of the study. So to revisit and simplify lets note I don't think the paper claims successful city=highly inelastic housing stock.
Me: Why aren't businesses moving to cities with more sensible regulation.
You: White Rural america is dying
Me: I wasn't talking about rural america.
You: Success means higher prices.
Me: It does? The paper doesn't claim that.