Here's a crazy idea: some malign forces, probably Chaos cultists, have some evil rituals that requires 'the blood of emperors' - the blood of a line that contains an emperor is sufficent for their purposes. But you need to sacrifice a lot of individuals for the ritual, some in pretty visible ways, which makes it difficult to pull off. Luckily, the line of Dieter is both weak and hated, and hopefully no one will put too much effort into finding their killers before the ritual is complete. That's a better fit for the kind of thing the Light Order deals with than some political assassinations, which is Grey Order business. And it might not even be true, but if Alric believes it to be true that might be enough for him to see this as a project worth taking on to shore up his position.
Baseless speculation, yes. But who knows?