You know, the spectrum you lay out is probably correct regarding people's
claimed viewpoints... but somehow the
results of (1) in particular never seem to line up with the claims it makes.
(1) and (2) form the sort of classical belief spectrum on the value of social-welfare programs. (2) just doesn't support these programs, for the reasons stated above. But (1), although supporting such programs generally, doesn't seem to support the kind of programs that would properly line up with their professed beliefs.
If the problem with a lot of homeless people is that they have "poor work ethic"... well, we've medicalized that, it's called ADHD and you can throw medications at it. But there are no social-welfare programs to get homeless people into psychiatrist's offices where they can be given free Vyvanse samples.
Instead, such programs seemingly only ever consist of 1. paying the homeless person's basic living costs—through free housing, or free meals; or 2. giving the homeless the opportunity to work and job skills training to potentially begin earn money for themselves.
Programs in the first category might indeed help people who are stuck in a temporary rut, and just need the details of "where food will come from" and "where they will sleep at night" handled for them until they escape it. People who are homeless because they are in the depths of a major depressive episode might find value in these, for example.
But the programs in the second category seem to serve nobody effectively. If you don't have any work ethic, teaching you how to do some particular job isn't going to make you start doing it; nor is lining up interviews; nor is even shoving you forcibly into employment.
The people who have some level of work-ethic escape homelessness eventually whether they receive any social assistance or not. The people who have a persistent lack of work-ethic will not escape homelessness no matter how many "free things"-style and "work opportunity"-style solutions you throw at them.
Those claims sound oddly more like what people on the (1) side of the argument claim, doesn't it? But this is the "steel-manned" version of (2): that people who fail to attempt to gain employment do not do so because they're irredeemably flawed; but rather because they need solutions to a work-ethic problem they're having, before any solutions to their poverty problem would have any potential to stick.