Idk how daily practical it would be. But you could mount wood/door with hinges at the bottom and latch at the top, then put as many hooks as you could fit. Then when you want to pick one, pull it down and you have a little necklace hanging garden. Granted it would probably still look a bit cluttered when latched.
Curtain rods with hooks might also work, could do 2 or three across the whole wall. Put the ones you wear least at the top and maybe need a step stool. Benefit of being flatter against the wall and being able to slide them up and down the rail to look through them.