Shelter should be, but doesn't need to be housing. When people fear that public transportation becomes shelter they're not arguing houses will be built in train stations.
Having other places with a roof, some security and some public amenities should go a long way to avoid other services getting bogged down by homelessness.
homeless people are already trying to build that but the so-called "protectors of law and order" keep showing up with bulldozers for some reason, as if they actually want people to be sleeping on public transportation instead of in their own private tents. This is probably because they get paid proportionally to how many people they catch sleeping on public transportation.
people don't want to live in shelters. they don't provide enough safety or privacy. being out on the street feels safer. any housing must at least provide a private room and bathroom. and ideally not have all those people concentrated in one place.
an important factor in improving your life is integration in society. but that only works if you live among people already integrated, not if everyone around you is also not integrated.
the same reason why it's hard for people to escape poverty uf everyone around them is poor too.