No one has said this directly (hopefully not because it's wrong, but I'll soon find out), but it seems like MZFW is simply a way of limiting the amount of weight in the fuselage. Because weight in the fuselage creates more bending moment at the wing roots than fuel in the wings, it would be possible to have an aircraft below MTOW and still overstress the wings. By limiting the total gross weight minus the fuel weight, MZFW ensures that doesn't happen.
Again I could be wrong, but I said that fuel in the wings contributes less to the bending moment because I assume fuel close inboard would increase that moment, even though fuel outboard would decrease it.