It's not even a healer/tank decision. A decent DPS player is just as capable of noticing the party is under pulling. Not to mention a lot of tanks/healers seem (rightly) unsure if they can rely on ranged DPS using their limit breaks to trivialize the last stretch, so you see a lot of unnecessary hesitance to pull big, so it's kind natural for the DPS to take charge there if they know they are going to LB.