From what I know about homelessness, is that yes, people are often homeless by choice.
If they go to say a shelter run by a Christian/religious/service organization. Hell even government-run, they have rules. As in no smoking, no drugs, no drinking.
That's fine for someone down on their luck, but for a hard-core addict/alcoholic, they are not going to play by those rules. They'd prefer to sleep outside if they can continue to use.
One of my favorite documentaries is called Dark Days. It talks about the tunnel people of NYC who live underground. These people live in hand built shanties, have tapped the electricity, and water lines, and basically live off the grid, drinking and drugging themselves silly.
But oh, what a dangerous place.
They've got their rules, and talk about some extremely freakish human beings. Some folks never leave, they stay down there for years.
The strange thing is that, despite it being so successful that Seattle actually brags about it, nobody else has tried to repeat the experiment.
It seems to me that more Republican cities would jump at an opportunity to save a bunch of money while reducing their homeless problem.
But there are a lot of people who would have sleepless nights over the idea of alcoholics being allowed to remain alcoholics, with no effort at persuasion or coercion to make them stop.