The high costs are because an area is desirable, not because it's dense. Density is how you do something to mitigate the high costs of a place like NYC. Imagine if you chopped off the upper half of all buildings there, what prices would do!

You could build a bunch of dense housing in Burns, Oregon and you wouldn't be able to charge much for rent there!

It's a bit of a chicken and egg thing because the density is a huge component of the desireability.