Kuruma Ebi, pastel drawing by chef kaz matsune
(originally post from quora.com)
We do use Swordfish for my sushi - both Nigiri and Sashimi.
Belly part is especially tasty and is a good substitute for Toro. The one I use is caught sustainable way in San Francisco (local for me).
The reason why it's not so popular is unknown.
In Japan, they prefer regular Tuna/Maguro, so not so much demand (as sushi item) for Swordfish. (It's normally cooked).
The reason there is no shark Nigiri or Sashimi is because it needs to be extremely fresh to be able to eat raw. The shark blood contains urea, which is decomposed over time and emit ammonia odor.