The homeless debate, especially around housing, has become a nightmare of semantic creep and rising metricism [1].
Metricism is the tendency to focus on measurable things; in principle a noble goal, but more often than not you can't actually measure the thing you're interested in, so you measure something similar and then pretend you're measuring the thing you want, and when you're done, you've implemented solutions which reduce your metric but have no effect on the underlying problem.
What is the problem of "homelessness"? Is it transient homelessness, where people, through a run of bad luck or circumstance, find themselves unable to afford housing, but otherwise are functional in society?
Or is the problem the much more visible problem of mentally ill and otherwise unstable individuals wandering the streets and pushing kids on to subway tracks?
The latter is the homeless problem that people care about (I mean, we are human, we care about both, but if I had to choose which one I'd rather fix, as a New Yorker, the latter takes priority). Fixing this problem, though, is incredibly hard -- there's the intersection of human rights, involuntary confinement, and the otherwise incredible complexity of managing mental health in a free society.
But this is SOOOOOOO hard to measure! It's much easier to just measure the people who are "unhoused", pretend you're solving the "homeless problem", and show that you can make the numbers go down. The problem being solved by increasing housing and lowering rents is not the problem of people walking down the subway screaming about electricity and knocking cell phones out of people's hands -- he is more than a couple of rent payments away from being okay.
[1] metricism is my own neologism; closest analogy is James C. Scott's "legibility" or Goodhart's "observed statistical regularity" or even the drunk "looking for the keys where the light is good" but I'm more specifically concerned about fetishizing around metrics specifically.