Did you think I was talking from Perospero's end? No. Carrot is the one with vengence, not Perospero. The only comment he makes is that because of his right arm, he gets annoyed about Pedro and would take out his frustrations on those associated to him. That has already been stated. The conflict was from Carrot's perspective since Perospero was the one that caused the situation the Straw Hats were in and forced Pedro to blow himself up to save the lives of the Straw Hats.
You seem mistaken to think that Pedro didn't "need" to blow himself up. It was a sacrifice that did end up saving their lives. Luffy was preoccupied fighting and getting manhandled by Katakuri, Jinbe was with Nami trying to get the Coup de Burst to start up, Chopper and Brook were already encased in candy, and Sanji went off to help Pudding and Chiffon make the cake. All the while, Big Mom was drawing closer to the Sunny. Luffy already demonstrated that Perospero's candy armour is susceptible to fire, and he bought time by slowing down Big Mom and temporarily incapacitating Perospero through blowing himself up while freeing the Sunny as well as saving Brook and Chopper.