Twenty five years working with the California courts left me confused at times, but not about the difference between being homeless and being destitute.
My perception of this is clearly different from yours and may originate from a having a different take on it, based upon what I saw during my career years.
Most of the homeless I ran across in those years were what you might call the “traditional” homeless most are familiar with: (often dysfunctional) people who are (and sometimes elect to be) homeless due to their lack of job, social or intellectual skills. Some had been homeless for many years and were long out of the job market - if they were ever working at all. Think “city panhandler.” Few of these folk have either ID or DL.
There was a second variety of homeless who were mostly middle class or working class people, rendered economically homeless due to financial hardship, job loss, layoff, spousal abuse, etc - families with children often fell victim to this. They often ended up in public family shelters, at least for a while. Many already had ID’s or DL.
A third variety of homeless was single middle class or working people, mostly men, who had lost their jobs and had no emergency place to live, other than on the streets. Again, mostly with ID or DL prior to their financial reversal.
Some of these homeless middle class and working people, at some point ended up living in their cars, if they happened to own one before their financial misfortune happened. Clearly the adults had a DL most of the time.
What I defined as “destitute”, which you may disagree with or not, were people as yet not homeless, but without much day-to-day cash due to low, or no, income. These people sometimes owned their homes or were living in places where they were allowed to stay for free or very little cost. These people were often well into adulthood and were sometimes elderly people: couples and some families as well as a few single people made up this category. Most of them were former workers or middle class folks and often had cars, though not always, and generally could provide an ID or DL.
So my point is, what category was the OP describing? Answer: the OP’s question was about homeless people. My response is based upon what I’ve seen the homeless community to be mostly about. Of the homeless I’m familiar with, most of the homeless that might not yet have a license were either in the first category (“traditional homeless”) or were children of the second category (unemployed middle/working class families), who were as yet unlicensed but now of the age where they could apply to have one.
I’ve seen no hard figures to support this, but my best estimate is that the “traditional homeless” people out there, well outnumber the “grown children of homeless families” category…at least they did when I was working (1972-84 and 1994-2008) in a field that gave me some contact with these communities. Given those probable numbers, I figured that the OP was as much talking about the need for ID for the chronically homeless, as he might have been talking about getting drivers licenses for the relatively fewer middle/working class homeless.