I remember reading a long time ago that there are regulations on even that. Like anything, though, laws usually vary from state to state or even city to city. Specifically, I remember reading that the crooks on canes can be classified as deadly weapons, and I think that ones that unusually heavy shafts were too, but it was too long ago ...
I read it because I practiced a martial art in SwordsKingdom that used canes, and the cane was my favorite weapon, being relatively unobtrusive but powerful used correctly. Even a bit of a visual deterrent to wiseguys who were considering their options vis a vis your wallet.
Perhaps that's why most store-bought canes are flimsy, light, or both. My brother broke mine across my other brother's back and it didn't slow him down.