Certainly if humans are a race in constant strife with their parents - brought to physical mock-combat by misunderstandings about things as simple as wizards and harlequins - then it follows that trolls are a species defined by their grief. Being systematically separated from their genetic forebears and forced into the custodianship of hostile monsters by a ruler who resents the very idea that a child might know their parents, scattered into the stars as far away from their biological mother as possible by an absentee queen under the thumb of the evil stepfather Lord English, defines who they are as a people.
So where the humans’ conflicts with their denizens represent the strife between themselves and their guardians, the relationship between the trolls and their denizens can represent only that same grief. It’s why Karkat believes that HUGE UGLY MONSTERS ARE FOR KILLING, PERIOD, and Vriska thought it was for the best that they all be rid of them as fast as possible. The trolls’ denizens are cursed to die for the same reason the lusii are; the denizen is a manifestation of the parent, and to a troll, the parent is dead.