> should be more expensive to live there

I didn't say anything about should or shouldn't. I was putting forth the idea that it is uniquely attractive to companies and workers. If housing were a normal market, supply would rise to meet demand, and the market could arrive at some sort of equilibrium. The present situation only serves rent seeking interests, and I believe that as a matter of public policy we should prioritize a broader set of stakeholder needs. On a macro level, prioritizing the interests of rent seekers is economically sub optimal, and transfers wealth from workers, companies, and consumers to land owners.

More expensive, yes; exponentially more expensive, no. Those market forces alone don’t account for the cost of living; that’s entirely down to zoning laws preventing high- or even medium-rises.