"(In the city where I live, the only wooden walking sticks--excluding crooked canes--are carried by the homeless. Not sure why.)"
I grew up in Washington D.C., and it's still my town that I live in the Maryland suburbs of. A lot of my time is spent downtown as I call it, and I can answer you on the sticks. In some of the less affluent parts of D.C., you will see a lot of rustic wood sticks being carried by the guys on the street. It's not a secret that a good stick isa heck of a legal weapon. The knife is the weapon of the street punk, and usually it's a stolen kitchen knife. A three foot piece of oak, hickory, ash, or hornbeam beats a paring knife any day, and the guys on the street know it. The stick carried openly is sending out a message; yeah, you can try to rob me, but there's going to be a fight." It seems to work for the people who have to live in the not so nice neighborhoods. The street punks who pull the muggings are basically low life cowards, and won't go against a victim that looks like they will fight back. Doesn't matter if they outnumber him 2 or 3 to 1, they are cowards looking for a no fight meal. Way easier to flash the knife at a brief case carrying guy in a nice suit who will be scared into handing over his wallet and cell phone, and then they are out of there.
There's also the sport of 'bum kicking" where a group of young street slime assaults a homeless guy for no real reason, other than cheap fun. A stout club is a nice thing to have. It's a viable weapon for the homeless that doesn't cost anything, is legal everywhere, and is effective if you halfway know what you're doing with it. Beats a screw driver or paring knife.
Cruise around any big city, and the closer you get to the low rent district, you will see more and more men walking around with a stick. Not using it to walk with, so it's obvious they don't need a cane, they are just carrying it. It's their way of broadcasting the message "Mess with me and there's going to be a fight, and I'm ready to start swinging."
It works. Kind of like part of the city culture.