There is no population that actively rejects any form of housing (cardboard boxes excluded) and if there is, they definitely aren't moving to large urban areas en masse.

And even if it's the case that they were formerly sheltered but 'decided' to be homeless again, it's probably the shelter provider that didn't do a great job at accommodating them.

In any case, cultural opposition to housing is a pretty weak argument to make in order to express despair where your valuable taxpayer money goes to.