Pet is a rather interesting term. The Hive worms seem to possess just as much intelligence and wit as any other sentient being. While the in-game depiction of Hive makes them seem like brutish uncivilized creatures, we have to remember their vast repositories of knowledge (World's Grave) and even their deep understanding of the arcane. Savathun spoke to a Thrall of her plans and it seemed to follow along without much issue. I have no reason to believe that the worms are any less intelligent as they, as a race, have learned to con other races into feeding them in a perpetual downhill sttuggle. Xol, Eir, Akka and the other worms are just the upgraded/ascended versions of what these larvae once were. Having a "pet" worm would probably be as damning as having the dead one the Osmium King once possessed. I imagine we would hear their whispers constantly just as with having Ahamkara bones.