A Death Star, or its later multi-targeting equivalent the Starkiller Base, seems to have only one function, namely destroying one or more planets, and perhaps their suns too.
But the Dark Lords that I am familiar with are driven not by a desire for destruction, but for rather power and domination. They use their Death Stars as weapons of fear, as threats, rather than having destruction as their end goal.
I wonder if there aren't more effective ways to achieve this.
The Dark Lords always have huge armies of stormtroopers, huge fleets of ships, as well as traditional and force-enhanced torture techniques. I would think that these tools would be sufficient to terrify planets and "bring them into line".
Not to mention the numerous unmentioned alternatives available to threaten populations with, such as poisoning environments, coercing officials, creating eclipses, force-choking beloved celebrities, and deploying atomic weapons (which, if discovered, could destroy a planet for a fraction of the size and cost, and avoid the single-point-of-failure).
We know that these stations take a long time to build, and must be hugely expensive. And we also know that every one built so far has been destroyed by Light-siders.
So why is the Dark Side so obsessed with building planet-destroyers of unimaginable firepower, and what makes the alternatives so much less appealing?