The Death Star is the apotheosis of the Imperial Navy’s drive for dominance of the Imperial Military, and the Imperial Navy’s single-mindedness about their “Technological Terror” is evident throughout the series. With it, they guarantee that an Admiral will always be at the helm of the “ultimate power” in the universe. Despite the Army’s (accurate) objections that the station is vulnerable, the Navy convinces the Emperor to build not one but TWO different battle stations that can be destroyed by a small fighter shooting a single shot.
The Navy’s fixation is almost pathological—when Leia gives up the supposed location of the Rebels on Dantooine, the logical next step would be to go to Dantooine and blow up the Rebels. If Leia is lying, they can always come back to Alderaan and threaten to blow it up again. To Tarkin and the pro-Death Star faction, however, demonstrating the “full power of this station” is the most important objective of all. Dantooine is “too remote to make an effective demonstration,” so they blow up Alderaan and lose whatever leverage they might have over Leia.
It’s not surprising that Storm Troopers never hit anything – their blasters are made by whichever contractor has the most political clout with the Imperial Command. If that contractor turns out a lot of defective blasters, the General who selected him certainly isn’t going to be the one to report the news to the Emperor and it’s not like the Storm Troopers are going to complain to Darth Vader or ask "60 Parsecs" to do an independent investigation.