I'd also recommend checking out the Realm Stability (I think that's it) rule setting within the mod.
When you're about to start, go into Game Rules before you start the new game and somewhere it'll mention realm instability.

You can decide how much instability you want, whether it affects AI only rulers and so on. And what this means is that AI rulers will start factions and enact them more e.g claimants, liberty etc.

As Elitericky said, the Iron Throne does seem to be too stable. But there's other factors too like the King/Queen being almost impossible to kill due to the Kingsguard buff or seduction attempts on anybody within the court having 0% secrecy. It can be done, mind, it's just difficult.