I don't know much about the loot table and how looting affects them. I do know that the looting enchant should increase the number of shells you get.

I have killed 15 shulkers (noticed I was barely getting any, so I ran a test case) on 3 separate occasions, all with looting III on a diamond sword.

Case 1: 4 Shells

Case 2: 3 Shells

Case 3: 6 Shells

Not sure what is happening, but most of them don't drop anything, even with a looting sword. This feels far lower than it should be, even If I didn't have the looting enchant.