The leader who decides to spend more time with their family [or the blackmail tapes get released], the sudden shift of power at the Nth Local Party Congress [after the funding for problem people vanishes], there are plenty of ways the Imperium could remove problems. And lots of those would provide lots of fun scenarios for players.
What about the injection of a 3I noble, who acquires stock and/or property and is able to begin influencing the area around their lands? The reception could depend on their aims and how they treat the locals under their charge. Plenty more openings for scenarios here.