I think most people understand this, but in reality many homeless do have a choice in their living situation. This idea that they can’t possibly have chosen their life reduces the homeless to human-like primates with no agency. Often they have a sense of personal dignity and are capable of making their own decisions, despite how destitute we see their situation.
My experience is from São Paulo and Seattle but entertaining this notion that it's a thought-out choice full of intention is wild. Most homeless people just want some shade of stability and would leave that situation any day any time if given resources.
They are not primates with 0 agency but most societies don't really give them a lot of options.