If the Hakurei have been yōkai exterminators for a long time, then they definitely have techniques that – in light of the new Gensōkyō – had become "forbidden" because they are very, very lethal to yōkai. With how lazy Reimu is, I wouldn't be surprised if she doesn't even know these techniques exist. She wouldn't need to. The current Gensōkyō doesn't need them.
Mizuchi would know, though... is this the real reason why she's so dangerous? She can give yōkai a really, really bad time.
