I would argue that the bags go to props. There are props being put inside of the bags and they are being used as props on stage. If they are simply accessories and are only there for aesthetic reasons I would give them to wardrobe.
Again, I would reference what many posters have mentioned above, that it's not our JOB or PLACE as SM to determine where the items go to. Each theatre will have their protocol for things like this, and even within that, it's the place of the props dept. and the costume dept. to determine this with the help of the production manager if necessary. But, we as stage managers shouldn't make these assignments on our own.
I do agree, however, that most theatres use the same logic that you mentioned, chops. If the item is being used as a prop (a bag, or a purse that's set onstage and thrown, or a shoe that lives onstage in the corner) it will probably go to props. If it's being worn at all, it will probably end up with costumes.
I think it's too bad when the unions get so upset about moving a drum across the stage and everyone thinks it's their job. The unions exist to protect us as artists, and in my opinion, spending 20 min arguing over something like that is petty and unnecessary. Someone just move the drum! Everyone else, enjoy the 10 seconds that it takes for them to move it and have a sip of coffee!