I get two impressions, but they're kind of vague, not very well-founded. One is of Cain not wanting to admit it's a powerful paramilitary organization. I think he wants to think they're just stopping the occasional disturbed individual, not that there's a big problem. Even after three "incidents," it took something big enough to call a "war" before turning it over to a specialist.
The other is of the Hunters being really difficult to lead. In the X profile here, twice they've used the phrase "leader-like figure." It makes sense for X because although he's very influential he never had a higher post than squad captain. But, peeking ahead, I see the same phrase in Sigma's profile, where it makes less sense because he was the leader, or at least he was supposed to be!
I could swear that I heard a council started up the Hunters, not Cain
Right here in the same book, on the previous page! The only thing I can think of is maybe Cain gets an honorary position on anything having to do with Repliroids.