The motive of Destroying a thing, organization, person, or place, is usually pretty straightforward. The goal is not to replace the thing with something else and it's usually not to make the thing or person suffer, but rather to remove that person, thing, place, or organization from the current plot equation. Under most circumstances, the removal of the target will either prevent some tragedy or remove opposition to another goal, which may be to Rescue the Love Interest or Join the Hero (or, if you're the Chosen One or Rightful King, then your goal of Destroying the False King or Black Knight will serve as a step on the way to your Chosen Destiny or Rightful Throne).
This goal isn't often very elaborate, though the steps taken to achieve it can be. For example: in How to Train Your Dragon by Cressida Cowell, Hiccup needs to Destroy or Remove the Seadragonus Giganticus Maximus from the beach of Berk. His steps to achieve that goal were convoluted and even amusing, but the goal itself was really very cut and dry. There is a massive dragon where it should not be, and he needed to make it not be there anymore. (In a similar way, once the Hooligans have landed on the nest island in the movie of the same name, Hiccup's goal is to make the Green Death go away or otherwise cease being a threat.)
It's also worth noting that this goal very rarely stands on its own. It's usually part of a larger plan, and only stands as a goal by itself here because it often represents a large part of the hero's journey, even when the final destination is a goal that can only happen after the mission to Destroy the target has already been achieved.
Another example might be the mission to Destroy the Death Star, which I trust we are all quite familiar with. While the goal of that scene is to remove the immediate threat (the planet-destroying space gun as big as a moon) the larger goal is to replace the Empire with a new Republic, which can't happen until after the Empire has been disarmed.
So here's the question I have for you this week, as I trust you've read books, played games, and watched movies that I have not:
Can you think of a story in which the goal to Destroy the Target has stood on its own without any supporting or overarching goals? I look forward to seeing what you guys come up with.
Until next time, stay awesome, Inklings!