No permanent address is self reported. In general those who aren't employable are unreliable for self-assessments as to why (although I don't doubt the lack of address is a hinderance -- for sure it would be).
Similarly, lost job tells us little about the bigger picture. What led to them being a lost job away from being homeless? Was it living beyond their means? No family? No friends willing to take them in? Being raised poor with no social net and working jobs making no money?
You have to really do a deep analysis to get in deeper to understand how people ended up in the situation they did, what roads they could have taken but didn't, what are societal ills that brought them there, and thus what to ultimately do about any of it.
Given the amount of money ($1B+) SF spends on homeless yearly, personally I wish we could find a way to use that to actually do something WPA style and employ them to do various jobs to actually improve things (and hopefully their life as well) versus just continue to maintain status quo.
You're right, depending on how you itemize things. However, there's $1B+ spent on human welfare and neighborhood development [1], much of which crosses over in one way or another either supporting the homeless or trying to not make people homeless with programs like food banks. If you look at where that's going [2], you'll see the areas with the highest unemployment are getting most of these funds.
Top cited primary cause of homelessness: "Lost Job" (26%)
Top cited obstacle to obtaining employment: "No Permanent Address" (28%)