Huh... now that's an interesting setup. That the Hakurei initially just tended to the shrine, and the actual yōkai exterminators were the Miyadeguchi. "Hakurei exterminators" are revisionist history. Reimu's techniques are actually appropriated from the purged Miyadeguchi!
I still think it's a missed opportunity to not involve the Miyadeguchi clan in the grudge – though I suppose an Uchiha equivalent would be too obvious.