Shark fins are considered a delicacy and a cure for many health issues - that is why the Japanese only take the fins. They make good money on the fins and therefore don't bother with the rest of the fish because they would make a much smaller profit for a lot more work, storage, processing etc. etc.
Obviously, as with any animal, the baby meat is nicer. But definitely folks eat larger shark meat too.
I had no idea that there was a meeting about the shark tournament - since I understand there is no shark tournament.