DC I am not going to argue with you about the homeless people you have run into in the Bay area, I haven't spent anytime there. In Texas there are plenty of homeless just as you describe who are just looking for your change or a buck or two so they can get their next beer, joint or fix of what ever drug they are hooked on.
But go spend time at the shelter, see and talk to the mother with three kids who ended up homeless because the husband left her , took what little money they had ran off with it and the car. She gets evicted after 90 days, and ends up in the shelter. Your statement about you can only be homeless by choice may be correct, but in some cases it was not a choice that was made to "intentionally" become homeless as you imply, it was a choice ended up being the wrong choice that resulted in homelessness.
The recent hurricane caused a bunch of homelessness here, people lost everything, they didn't choose to be homeless intentionally, they chose to live in an area that had inherent danger in the form of flooding, they might or might not have known of the danger, but they did chose to live there.
The stories and situations are numerous and could be debated on and on, my position is that we all need to pitch in and help the ones who at least want to be helped.
My pointing out the turtle and the homeless situation was to show that the homeless aren't even showing up on the radar screen of the media as far as suggesting to the public to help. The media will report the deaths, and report the effort to move them and that is about it here.