When is making me think it could work differently is these necklaces that give the world of one school and the prism of the opposing school. If the world/bubble bonus is calculated before blades/traps, then I'm not seeing the benefit of these necklaces. However, it the world bonus is calculated after traps, that it makes more since.
My only other thought, is that these are intended for making giant trap chains like: ice world+ice spell>ice trap>ice prism>fire trap>fire prism>ice trap. The necklace would mean you would only need to train or use treasure cards for fire trap.
Just an added point. The use of the opposite school prism with a global for your school very useful in certain boss fights. Just an example. If you are Storm and fighting Hades in Tartarus. You cannot cast a single prism on Poseidon so you have to use Multi. This causes a problem for Zeus because he's Myth. Solution, cast a single myth prism on Zeus, then cast the storm multiprism on all, then your Sirens or Tempest can kill all with the correct school.