MZFW is a structural limit, nothing to do with performance or handling. The wing design load for many aircraft is a 2.5g manoevre at MTOW and fwd CG. The wing has to carry this load but the inertia loads associated with wing fuel give wing bending moment relief.
So long as the wing tanks remain full one can juggle between MZFW and centre tank fuel maintaining the same MTOW without affecting wing design loads.
If, still at MTOW, you try to push MZFW above the point where there is no centre tank fuel then you will need to take fuel out of the wing tanks, the bending moment relief will be reduced and the wing design loads potentially exceeded. To respect the certification conditions in such a case MTOW will have to be reduced. There is a snowball effect which means that the MTOW reduction is greater than the MZFW increase. In the graphic posted earlier for example an increase in MZFW of 11T was accompanied by a MTOW reduction of 27T. One can therefore exceed MZFW at the expense of MTOW IF THE MANUFACTURER HAS PUBLISHED THE EXCHANGE RATE otherwise you are guessing and illegal.
However, nobody has mentioned the fact that increasing MZFW above the manufacturer's value will increase the fuselage bending moment in the event of a hard landing. This is particularly relevant because the additional payload can be distributed all along the fuselage and give rise to large bending moments near the wing box. There is no way to relieve these inertia loads.
Statistically, hard landings are more likely than pulling 2.5g in the initial climb.
MZFW is there for a good reason and must be respected