Funny. Reading this I went off on one of my random little tangents imagining Mook, after being confronted on the street, saying, "Hey, want to see a magic trick? Lend me some quarters to put in this bandana... see, I tie them in this little knot, and now watch what happens!" Bada-bum.
Regarding improvised weapons, I do think you can train a state of mind where you are aware of many potential weapons in your environment and have built up the martial skills to use them effectively. In one of the systems I've trained, Latosa Escrima Concepts, that mental and physical adaptability is referred to as "transition" -- one of their five fundamental concepts for self defense.
IMO, developing this kind of adaptability is far more useful in daily life than developing weapon-specific skills and having to "carry". Or you could be like one friend of mine. He goes everywhere armed to the teeth. He always carries a concealed 9mm and a couple of tactical knives. Even when training. Yeah it's legal here, but talk about a pain in the butt! And then what do you do when you have to go somewhere where you can't legally carry?
Frankly, I'm with Frank on this one. Your brain is the weapon. Your body and anything you can get your hands on are "accessories'.