Maybe the reason you are confused is that dayshapes are so rarely seen on sailboats. This is not because they are not important but because the owners don't have them, don't think it is important to use them, or are ignorant of the regs. and the shapes purpose.
The last thing any mariner wants to be saying is, "what's he doing over there?" For instance, you really don't want a freighter changing course, possibly moving out of the shipping lane, for a sail-boat under power with her sails up as this can create new crossing situations for other vessels. The sailboat becomes a power-boat the minute she starts her engine and loses her right-of-way status. The only way other vessels know this is by her flying the black martini glass (inverted cone).
Anchoring presents much the same situation. You throw the hook over the side, in an area vessels rarely anchor, to deal with an emergency below decks and, by flying a black ball, other vessels know that you are made fast to the ground and not manoeuverable.
Displaying proper lights and shapes, and knowing their meaning is essential for safety; your safety.
That freighter heading towards you, flying two black balls or showing red over red at night, is not going to change course! Even for your sail-boat. She can't change course-she's not under command. Probably lost the engine or the steering gear went out and you'd best be movin'.
Dayshapes come in collapsable canvas and mesh configurations for easy stowage.