I read the book 'Homelessness is a Housing Problem' by Greg Colburn recently, it has a lot of data and makes a good argument for this position. A good direct comparison is between Seattle, WA and Charlotte, NC... they've both experienced a ton of growth in the last couple decades, but Charlotte's more favorable geography has made it much easier to build housing to keep up with this growth.
You can also look at places like West Virginia, or Balitmore, which have high rates of crime/addiction but low rates of homelessness- housing is cheap over there.
But isn't the crime and livability correlated such that low crime areas like Seattle are more desirable places to live. And, that's why housing is more expensive?
Baltimore is very high crime and as such inexpensive and as such low levels of homelessness.
You can also look at places like West Virginia, or Balitmore, which have high rates of crime/addiction but low rates of homelessness- housing is cheap over there.