Because of NIMBY. Basically the rich people at the city's center won't let regulations pass that would increase density and therefore more poor people living ar

Because of NIMBY. Basically the rich people at the city's center won't let regulations pass that would increase density and therefore more poor people living around them. They like the current status quo because "they got theirs". They limit what kind of housing can be built, how tall it can be, etc and price out all but the richest land developers who in turn charge ultra high rent for the limited housing. I don't even think they necessarily need to build "poor" housing as much as loosening regulations and allow other than historic buildings to exist.