Most homelessness is also temporary, with around the same range of 80% moving on within a year.
That being the case, the value-added of free housing appears marginal compared to the cost. It would best target those who are a) chronically homeless, but b) neither addicted or mentally unfit to be employed, which sounds like a vanishingly small demographic. Mind you I take "effective" and desired outcome here to mean that they won't continue to roam out in the streets, either to be close to dealers or from being mentally unwell.
There is a bunch of it depends there. California has more homelessness than other states. Part of this is in some areas housing is so expensive middle class people cannot afford to live there, but they can get jobs there and so being homeless is often the only option if you don't/can't leave. Part of this is California has a fairly mild climate (well in the places people live): you won't be comfortable some nights, but the weather won't kill you.
States with lower housing costs do appear to have lower homelessness rates.
That's right, it scales most closely with housing cost. That tracks with homelessness generally being temporary, being priced out. California is also infamous for rent control policies in NIMBY cities that have been an abject failure. The supply of rental units was low because they are artificially risky and promise too little in return.
Zoning and regulatory reform spurs more building including smaller, dense units, which lowers prices. There's a fantasy among leftists that developers are snubbing mixed-density and dense mid-rises because condos pay more. No one leaves money on the table. Everything is built on credit, and banks deem these builds riskier in large part owing to the impact of zoning and regs. Condos have a lot of overhead, which checks a lot of boxes, while this would be unaffordable for other units. They also ignore that there are small developers in cities that try to compete, but can't get loans, because of these regulations.
That being the case, the value-added of free housing appears marginal compared to the cost. It would best target those who are a) chronically homeless, but b) neither addicted or mentally unfit to be employed, which sounds like a vanishingly small demographic. Mind you I take "effective" and desired outcome here to mean that they won't continue to roam out in the streets, either to be close to dealers or from being mentally unwell.