That is not precisely accurate. Ayakashi may be fought with the full power available to any god or shinki, but they cannot be permanently destroyed save with 'Rend'. That may only be conducted by a god wielding a shinki in vessel form.

[Of course, one might call a divine weapon 'unconventional', but the principle applies to more than the goddess.]

Fighting them is necessary to weaken them, in fact, so that they may become vulnerable to Rending.