I don't think it's weird. We're facilitators to ensure the ritual is complete, but that doesn't necessarily mean we're the only ones who have a motivation to go through with killing. We can use it to our advantage frankly.

[Because if not for Kamui, Tsurugi would likely be dead now.]

Yeah I agree. It's too risky to trust people who aren't in our group. You never know who will try to get rid of you - people are surely forming alliances.