Think of it as similar to Hiroshima and Nagasaki.
One problem with your comparison. Hiroshima and Nagasaki were done as a last ditch effort to shock the Japanese into surrender so that the United States wouldn't have to fight a costly island war with millions of potential casualties - as well as to make sure the war finished before Russia moved in in force and started annexing things (like Hokkaido). Multiple offers of surrender were sent and even the people who ordered the attacks were mentally scarred by them. They were horrified at what they had done, but they felt it necessary.
In contrast, the Empire fired the Death Star on Alderaan just... to test it. It wasn't their Hiroshima, it was their Manhattan Project. It was hardly a last-ditch effort to do anything, especially since Alderaan wasn't particularly threatening the Galactic Empire. The people who ordered the attack weren't even affected, because, let's be honest, they're cartoon villains. The destruction of Alderaan was hardly necessary to anything, they just did it because they could and because they didn't care about sentient life. The fact that you empathize with the cartoon villains and not with the Rebel Alliance says quite a lot about you, to be honest.