Soul Society is just a big area with no official ruler. The Gotei 13 is just a group of policemen set up by Yamamoto that helps to regulate a few things, but was not set up by the Soul King. The Soul King has been referred to as an "it" a couple times in the manga.

So lets just assume that the Soul King is a computer that doesn't take action unless the balance is threatened. Most of the time it doesn't care what happens in Soul Society because it sees the disputes as trivial compared to the grand scheme of things.

Lets also assume that Buckbeard knows this.

Now, move forward to where Sasakibe was killed. This event enraged Yamamoto, and it is exactly what Buckbeard wanted. During the "war" Yamamoto has gone ape shit and his Bankai threatens to destroy all of Soul Society. I mean he's on the verge of setting everything on fire, he's raised the dead to fight along-side him. What happens when he releases "North"?

Buckbeard is definitely stalling for something.

Maybe the Soul King will see Yamamoto as the only threat to Soul Society and smite him? As punishment his powers taken away?

Just a thought.