If it's not too much of a bother for me to launch into a bit of a gedankenexperiment with the setting, I think the "shikinami" carriers, the ones who use paper seals to summon planes, could still work well with the Witches. No, they wouldn't be able to carry a whole Witch around (well, they could, i.e. Lucchini on her back, but it wouldn't be of any practical use), but they could use their shikinami abilities to summon duplicates of the Witches involved in the combat, so that the Neuroi in question gets to play a short round of "Which Mio's the Real One?" before getting chopped to bits.

"This is probably a stupid question, but . . ."