Carbuncle's animations don't really fit the fairy skills. Carby's abilities all cause damage, and that's a big reason why he works as an Egi glamour. Lore-wise, Carbuncle is also more specific to ACN and SMN so even if it was a thing; it would just be, weird. For lack of a better term. I think if SCH was to get fairy glamours, a certain aesthetic would need to be maintained. I think true fairy glamours would have to be something similar to Seraph in that Lily would have to take on the appearance of another winged-type familiar.

It could be a dragonette, moogle, pixie, even a magical tome. Lots of possibilities that would be potentially wasted if they just went Carbuncle tbh.