My mistake, the 400 number is not correct as you point out. Still, even at 5km per km^2 it is one quarter the density of Seoul and one fifth the density of Paris. I've never personally been to Seoul but Paris still seems to have plenty of green spaces.
I don't doubt for a second that building a lot more housing is not possible for the foreseeable future but like in most places that is a political problem and not some fundamental constraint. And rent controls don't "solve" the basic imbalance between people wanting to live in a place and there not being enough housing for all of them in any meaningful sense. You are still rationing one way or another. When there are fixed supply constraints then maybe that is a more just way to do it, but when the supply constraints are artificial then it just entrenches a bad equilibrium.
I don't doubt for a second that building a lot more housing is not possible for the foreseeable future but like in most places that is a political problem and not some fundamental constraint. And rent controls don't "solve" the basic imbalance between people wanting to live in a place and there not being enough housing for all of them in any meaningful sense. You are still rationing one way or another. When there are fixed supply constraints then maybe that is a more just way to do it, but when the supply constraints are artificial then it just entrenches a bad equilibrium.