> The key thing to note here is that with very, very few exceptions, everyone living on the street was a 'normal' person. The line of being 'normal' and 'homeless' is startlingly slim.
I did some work with a bay area organization that runs reduced rate housing for transitionally housed people and families when I was in college. First, I should say that you're completely correct about the numbers at any given time, but this also misses the larger picture.
Homelessness, broadly speaking, breaks down into two categories: temporary and chronic. The vast majority (~90% by the number of people) are 'temporary' (generally just called homeless). These are people who lose housing for a short period, then find housing again. Around 10% of the homeless are 'chronically' homeless - which means they have been homeless repeatedly over a number of years.[0]
I bring this up because I think your impression of where our social safety net is failing is incorrect. We do pretty well when dealing with the 90% of non-chronically homeless people. I think we could do a lot better, but most of those people are homeless for a short time, get help and find housing and stability again. When you talk about 'normal' people who have had a run of bad luck - they are the group we do best at helping.
The chronically homeless, on the other hand, need a totally different set of services. Being homeless for a long period of time often changes your entire outlook on life. The idea of investing in the future, or of any long term planning, can start to seem absurd if you're not sure where your next meal will come from. In general, the idea of living 'in society,' where there are shared rules and expectations looses its value if society places no (or almost no) value on you. Chronically homeless people can prefer homelessness to free housing, they can refuse to participate in a process that will feed, cloth and employ them because they don't believe it will be better than their current lives. They often have PTSD. In many ways, we are still working to understand how to best help this population.
I point this out because it's important to understand the kinds of things we do well and the kinds of things we do poorly. The kinds of interventions that help the recently unhoused will often be useless to the chronically homeless. All people are people and deserve dignity and compassion, but we shouldn't focus too much on how much like us many homeless people are. The failures of our system and what most people think of as 'homeless' people, are often facing a totally different set of problems and have a very different outlook on life. They are just as much people are you or I, but we don't do them favors by pretending they're one missed paycheck away from self-sufficiency.
[0] https://en.wikipedia.org/wiki/Homelessness_in_the_United_Sta...