I'm still really inclined to think that the Miyadeguchi were the specialists, directly serving the Hakurei aspect of yōkai extermination – while the Hakurei clan itself worships the kami in more general, spiritually-oriented sense.
That is to say, a lot of Reimu's yōkai extermination techniques are actually Miyadeguchi's – and quite possibly watered down a lot too, since the current Gensōkyō probably won't be needing those 40k-level of anti-daemon arsenal anymore. The Hacureia Nemesis Force Naginata is probably gathering dust somewhere in the warehouse.
