I'm glad to hear that we are nicer than your average IT customer!
I think I understand visually what it would look like a bit better, but to me it seems tedious to have to switch the animations for all of the different pieces, which makes me think I'm missing something.
Like for instance if I want to switch from "idle" to "run" animation, I would have to tell the hair, the face, the iris, etc to switch their animations to "run".
Also how would you split each frame, is that done in engine or do you have to do it in a sprite editing program?
Would you mind telling me the official name for this method so I can try and find some documentation for it? I looked up paper doll method but it seems to be mainly referencing skeleton animation which seems different