Rogue One finally gave us the complete history of the Death Star — and we learned that, understandably, Alderaan wasn't the first target of the superweapon's wrath. It didn't take long for Rogue One to give us a glimpse of the battle station's power, as Moff Tarkin had the superlaser destroy the Holy City of Jedha. But given Imperial forces had completely abandoned the planet, one question has to be asked: Why did Tarkin only destroy a city? Why didn't he destroy the whole planet?
The Out-of-Universe Reason
Of course, the main reason Jedah was spared was a strategic one. Rogue One has to balance telling its own story with ensuring that the scene is set for the classic #StarWars movies, specifically A New Hope. So we see the Death Star completed, and the superweapon tested — but, for the sake of dramatic impact, Alderaan remains the first world to be destroyed by the Death Star.
In terms of the overarching narrative of Star Wars, this makes perfect sense; but that argument only takes us so far. For Rogue One to truly make work as a film, this question of narrative must be answered from an in-universe perspective.
Imperial Politics Spared a Planet
As we saw in Rogue One, as the Death Star approached Jedha, Imperial forces were evacuated planetwide. Orson Krennic's clear expectation was that he was about to get his chance to fire the superweapon; but, at the last second, Tarkin commanded him to only destroy the Holy City. But why?
The Rogue One novelization gives us the answer: Tarkin and Krennic were engaging in a political battle, with Krennic trying to take responsibility for the Death Star's success. So Tarkin set up the firing as a test — it would prove whether or not the Death Star was actually completed. If the Death Star's superlaser failed to fire properly, then Orson Krennic would be judged a failure, and Tarkin would take over full control of the project. This is hinted at in the film as well, but the novelization takes it even further, with Krennic actually taking measures to protect against potential sabotage. So bitter is the rivalry between Tarkin and Krennic that he fears Tarkin would sabotage the superlaser in order to undermine him!
Then comes Tarkin's masterstroke. He is protected against failure, but he is also protected against success. Had the superweapon been used to destroy an entire planet, this spectacular result would have been used by Krennic to illustrate his success. After all, Krennic had successfully completed the construction of the Death Star, and it had been proven to work! With the planet Jedha destroyed, the Tarkin Doctrine of spreading fear across the galaxy would have truly begun — but Krennic's name would have been the one associated with the success.
Instead of giving Krennic such a tremendous opportunity, though, Tarkin limits the superweapon's firing. In Imperial circles, the destruction of the Holy City would have been seen as nothing more than a test of the superweapon. There is no glory associated with this, and the powerful statement — fear the power of the Death Star, see what it can do! — is left for another day. To add insult to injury, Darth Vader later told Krennic that the destruction of the Holy City would be explained away as a mining disaster. Krennic would gain no glory from the test firing of the Death Star.
There's a very real sense of irony to the politics here. Tarkin protected himself against the Death Star's failure; he also protected himself against the Death Star's success. And Imperial politics just saved a world.
One of the reasons I love Rogue One is that the film's narrative works on literally every single level. No matter how much you dig into the plot, Rogue One is the gift that keeps on giving — every aspect of the narrative is so carefully written, the continuity is so very effective, and the most subtle of character-work runs through every scene. All of the above is implied in the film, but Alexander Freed's excellent novelization makes it explicit. I definitely recommend that Star Wars fans should pick up the book!