Note- This is a silly, dumb, and quite disruptive idea with regards to game balance.
That being said, this is the idea.
Blowing up planets is too small scale, the busy dictator needs faster ways to rid the galaxy of entire star systems. Specifically by blowing up the stars, now having a starkilling weapon would be a bit overpowered so I say just throw in like 60-100 logistics points worth of ships into the star and watch it go boom. What better way to express my hatred towards the Drengin than shoveling ship after ship into Drengi until it blows up? While I'm here, could you imagine the AI doing this, you're at war with someone, you're taking it to them, they've been plowing cash into building speed ships, you haven't even seen them whizzing into the Sun and then one turn boom, your home star system just goes poof. Because in space nobody can hear a boom.
Sorry, I just got tired of seeing so many threads about blowing up planets, I say if you want to blow up something big, blow up something really big.