Housing first is a proven strategy in dealing with homelessness. The fact that every state has not adopted these policies to help eliminate the homeless population shows this is more a cultural issue than a lack of housing.
According to the Census there are a lot more empty houses than homeless people. Let that sink in and you start to realize all is not what it seems.
Until someone is safe and has their basic needs met it is impossible to work on issues such as mental health and addiction.
The solution exists but it is going to take a lot of our time, money, and most importantly a cultural shift away from blaming people to accomplish it.
If we could fix our homelessness then we would show that we truly care about our citizens rather than just paying a lip service to our most vulnerable people.
I encourage you to lookup up Housing First if you have not already. While it may be misleading to say there are 16 million vacant home to half a million homeless people (32 homes for every homeless person), for the reasons you mentioned, it is entirely possible house these people.
No one who knows about this issue is thinking about warehousing people. Like you said they need a stable place to live, access to services, transportation, and work when they are ready.
Anti Homeless Architecture (lemmy.world)