Therein lies the problem. A large proportion of homeless fall into this category [*], and it's very hard to institutionalize people against their will. We like to think that most homeless are functional people who are simply down on their luck, and thus putting them in stable housing and getting them set up to work would solve their problems. But this is sadly not the case.
[*] This study [0] found that 80% of homeless people have some kind of mental illness, with 30% having severe mental illness. This is compounded by the fact that >50% have substance abuse problems.
Either you start off with the first principle that it's OK for wealth-transfer schemes to make tax payers 'worse off' via compelled charity, or I don't think you can get to the point of supporting generalized homeless relief programs. Maybe programs targeted at short-duration stuff to get people into jobs that are capable of doing them and a housing contract might work, but it'd have to be extremely well thought out and wouldn't benefit most chronic homeless.
IIRC, For decades, the homeless "relief" programs run by states like Florida, Georgia, South Carolina and others pretty much ended at bus tickets to San Francisco for the homeless (whether they wanted to go or not) and that's it.
Is it any wonder the population of homeless in SF grew?
[1] https://www.theguardian.com/us-news/ng-interactive/2017/dec/...
Reality is always more complicated than a one-liner. Surprise, surprise.
But that doesn't make it a "myth." Rather it's more municipalities and more disposable people being "disposed" of.
That doesn't make it right and certainly shouldn't normalize such practices -- that said, it's a little late now.
It does, though, and the article I linked explains what actually happens: people are not systematically shipped to any particular big west coast city. There are numerous programs in numerous cities which send people back home, essentially, to places where they have support in place and simply need a way to get there.
And I disagree with your analysis. That's not an attack on you or The Guardian for that matter.
While there certainly are programs as you mention, there are (and have been for decades) others that do not seek to reunite people with support systems -- rather they just want those pesky homeless people gone.
Out of sight, out of mind and all that.
I'll point out that this is a myth as many time as you repeat it until you cite some source to back up the assertion.
And what I cited is not my analysis, it's a reputable publication that did actual investigative journalism.