I would strongly suspect that since this is an SS model, the higher current rating is for the rapids, but, more importantly the spindle accelleration.
Lower rated wiring might be OK, or not. Consider how much voltage sag you will see when the spindle tries to go from 0 to 12,000 rpm, in three seconds. (whatever the numbers are)
The S machine was modified for rapid spindle start stop, fast tool changes, and faster rapids.
The amount of power needed for the axes will not be nearly as significant as starting and stopping the spindle.
IF nothing faults from low voltage on spindle starts, you might get away with it.
Any consideration about max cutting loads might not be the issue. Weather the wiring heats up during the three second (actual time??)spindle start might not be the issue.
Sagging the voltage to the control, or to the drives might be the issue.
You notice that the actual power ratings of the machine is not a lot higher than the non S model, but they do have a higher current rating. bigger wiring will not have as much droop for an inrush current as "adequate" wiring.