I actually do not think that is the answer from a lore perspective. I think the answer is supposed to be that the Destroyer is, as you have hinted, some sort of ephemeral Lovecraftian Cthulu-type world-eater. It emerges however often the Vault is opened, and each time the Vault is opened, a different form or iteration of the Destroyer is unleashed, but the Destroyer cannot actually be killed permanently because you would only be killing its current/present form, not the immortal being itself.
Or at least that is the best suggested answer that I have seen to my original question (i.e., how does the Destroyer still exist in BL3, when we supposedly killed it in BL1). That answer makes enough sense, I guess, but unfortunately I also find it kind of unsatisfying from a lore perspective, but eh - whatever. It seems to be the best explanation.