According the article linked below, NY City has had some success with Housing AND Treatment (drug or mental health or both), which for some reason is incorrectly called "Housing First". Success being defined as getting a large (not all) number of homeless off the streets.
Yes, it is expensive, requires caseworkers, social workers, etc. But when done right, it does seem to work. One thing it does not do is force homeless people to into the program against their will. And if every NYC homeless person did willingly enter the program, it would be vastly inadequate.
Funding seems to be a mix of city, state, corporate, and federal, along with a lot of volunteer work.
https://www.newyorker.com/magazine/2023/09/18/a-journey-from-homelessness-to-a-room-of-ones-own
Warning: Long read of a complex problem.
I found these snippets interesting (bolded is mine:
This strategy, known as “housing first,” was pioneered in New York, in the early nineteen-nineties, by Sam Tsemberis, a psychologist whose organization, Pathways to Housing, began renting apartments for homeless people with mental-health diagnoses and delivering medical and psychiatric services to them at their new residences—debunking the prevailing belief that people could not remain stably housed without having first undergone treatment. Study after study showed Tsemberis’s approach to be far more successful than requiring treatment in advance. Housing first became a federal policy in the United States with passage of the HEARTH Act, in 2009, though advocates say that its implementation is spotty.
...
New York State has the second-highest number of homeless people in the nation (largely living in New York City) after California, but whereas almost seventy per cent of California’s homeless live on the street (a sizable portion in vehicles), fewer than six per cent of New York’s do, making homelessness far less visible here. Many factors account for this disparity, chief among them the fact that New York City is the only municipality in America to guarantee a legal right to shelter for individuals and families—the result of court-approved agreements between advocates and the city that date back to the nineteen-eighties. (Massachusetts has a right to shelter for families.) Research disproves the notion that homeless people migrate to the West Coast for the weather; rather, a comparative paucity of shelter beds likely explains the more overt presence of homelessness there.
Anyway, if you really give a shit about homelessness and the drug addiction that goes with it, you should read the article.