Elrisse is a High Luminary, the highest level of Witch Hunter in the Light Order as well as an Abjurer, which indicates expertise in Daemon Hunting:
Horstmann is also an Abjurer and a Daemon Slayer. These options:
Are likely covered by their expertise. Neither Regimand nor Mathilde are proficient Daemon Hunters. They focused more on societal manipulation and subterfuge than Daemon Hunting, which is the Light Order's specialty.
If a sufficiently powerful demon manifests, I have no issue with letting Alric take a shot at it. Prior to that, Mathilde and Regimand are both more than capable of handling the investigation by themselves. Both are fully trained and experianced grey wizards, and Regimand specialises in infiltrating cults—not to mention being powerful enough to win a running battle with a tzaangor across hostile wilderness. Bringing in more people is no guarantee that we will get those chaos research actions for free—and then we will have spent two actions to make our primary mission more difficult.
Simply put: We are not here to humiliate Alric. We are not here to stop the murders. We are here to stop the investigation from exposing the truth about the Empress. Renegotiating with the Lights and pulling in more wizards does not help us with that.