Here's the situation in Montreal...might just be the same all around NOrth America for all I know.
There are a few hospitals in the area that deal with the insane and depressed. They have X number of beds. They have to deal with X + Y people. They can't, so some of the left over people get "weekend passes", that is...they get to go back to their families (if they have them or are acepted by them) or they get shown the door. They walk out and some of them come back...many don't. They leave with 2 days worth of pills...some actually take them but the nature of insanity is that you think that you're fine, and since you're fine..you don't need medication.
All those Y people are falling through the cracks in the medical system. Now, imagine that you're on the street for the weekend. You have no inclination to go back to the people who put you in there (family and friends), you don't want to go back to the hospital (effectivly a jail) and you're certainly not holding onto either the mental capacity or skill-set to get a job. Hell, you don't have a SIN# (Social Insurance) because your card is back at the hospital/home/family, you don't have money, you don't have an address to ship you SIN card to...no SIN card=no job. No job=no money, no money=no food, clothes, home, bus fare, copies of your CV, cash for a paper, etc... what are your chances of finding a job?
Minimal...and yet some do it anyway....only to lose their job because, guess what...they're insane. Oops...back in the hospital or jail. Get out of jail...same problems except that you now have a criminal record to help stop you from getting a job.
Some are lucky enough to have their families bail them out, or services, but most just keep falling through them cracks.
Look at the bums that you kick on the way to work...they talking to themselves? Why is that? Did homelessness drive them nuts or did insanity+society drive them homeless?
ps. Prof... I've had to throw plenty of homeless out of hotel lobbies and stairwells and back onto the street. Didn't like it, but I knew that my job was on the line. Never took any pleasure out of it, especially in the winter. Somehow I doubt that you did either...just pissed off that you HAD to do it as well, and pissed off that there will always be homeless people out there and more to kick out the next week. Oddly enough...you have a heart.