@Jill F. and @Dennis M. I agree. Mental illness- it helps to have better treatment, but even here, family support or sometimes friends need to be involved to keep people off the streets. Laziness and mindset: this comes at all levels, from the severely lazy who will not clean their houses to those who are not clearly in trouble, but who have no vision at all for their lives. The movie above shows a young man who is able to pay for a hotel but who can't find a place to rent. The hotel probably costs more than a rental and more than a mortgage. He's probably working. His girlfriend works. Apparently she was evicted once so this is the reason they cannot find a rental. As a landlord, these folks would be high risk. I would not particularly want to rent to them. In order to make it worth it, it would require a higher deposit than some state laws allow. Maybe one could collect an extra $200 in mid-month every month and keep in a savings account for them $5000 or so, to help tide people over- this could be used to pay the rent for up to two months, or for moving or storage expenses. A lot of times, in my observations, the problem is not lack of money, it is lack of savings. People can spend $5 per day on cigarettes or drugs, so they have money.
Also, a lot of elderly people are living on social security. If they had difficulty working due to a disability, they might get only $700 to 800 per month. Sometimes food stamps will only give them $15 extra per month. Co-living situations might allow them to spend $400 on rent and utilities, and they could get by.
For instance, here is a link to student housing in Chicago:
http://www.capstonequarters.com/
The rooms with shared facilities are as low as $475. Of course, shared facilities with mentally ill people will be problematic, but might work.
San Diego allows some parking overnight in public parking lots. Maybe there could be tiny houses, parking, shared kitchen, bath, and laundry facilities like in campgrounds? The price of land is too high in SD for this, but it might work in other areas. There would be problems, but many police departments today have specially trained officers who work with the mentally ill. The health department could put an onsite nurse at the site to help with the disabled and mentally ill.
It seems like there are more men than women who end up in this situation, though the reasons are not clear to me. Perhaps women are more likely to be in support roles for men who work while men who are not good at holding good jobs don't do as well? Part of the problem might be the loss of single room only (SRO) rentals in hotels and rooming houses.
Due to the reasons you mentioned, I believe that there will always be a group of people who just cannot make it on their own. The reasons don't matter. From a selfish standpoint, having homeless people camping out on the street is bad for property values and safety. Hiding our heads in the sand doesn't work.
I'm just throwing out ideas because it seems to me, that the people on this website probably would have more practical ideas about the housing parts of this issue than any other group.