NYC/SF are expensive because there are MANY good jobs there and people WANT to live there. Not because of the density of housing. You could build 500,000 homes in the middle of your empty field in North Dakota, and it wouldn't do much for the demand there. You aren't going to create Manhattan by magicking 3.5 million housing units of similar quality into the Red Lake Indian reservation in Northern Minnesota.
But overall you are right, that in the real world local density increases can/often lead to local gentrification/rising prices, and the benefits tend to be for the wider area. But the actual impacts depend a lot on the particulars and the services/jobs available.
NYC/SF are expensive because there are MANY good jobs there and people WANT to live there. Not because of the density of housing. You could build 500,000 homes in the middle of your empty field in North Dakota, and it wouldn't do much for the demand there. You aren't going to create Manhattan by magicking 3.5 million housing units of similar quality into the Red Lake Indian reservation in Northern Minnesota.
But overall you are right, that in the real world local density increases can/often lead to local gentrification/rising prices, and the benefits tend to be for the wider area. But the actual impacts depend a lot on the particulars and the services/jobs available.