Can cities ever actually fix their housing shortage?

Seems that loud activists always call for more population density and more housing options in cities. But none of the actual residents already there - especially the local politicians who control permits - have any interest in having more low income people in their neighborhoods.

Any area in which they put up a bunch of inexpensive apartment complexes immediately turns to a crime-ridden shithole that no one actually wants to live in.

Is there any actual way to fix this or is this just how life is now with increased population?