If the current carrying wires are upsized to reduce voltage drop, then code requires that the EGC be similary upsized so as to be no smaller than the current carrying wires.
The reason for this is open to debate. I can think of two reasons.
Firstly to reduce touch voltages in the event of a ground fault.
Consider an appliance with a grounded metal case that is connected to a grounded circuit.
Suppose that the appliance is defective and that a hot wire touches the metal case.
With the hot and EGC wires the same size, they form a potential divider with 60 volt drop in each.
The metalic case of the appliance is therefore energised at 60 volts, until the fuse opens, which might take some seconds. A person holding the appliance would get a 60 volt shock, possibly dangerous but more likely not.
Now consider a similar installation, but with the EGC much smaller than the hot.
During a ground fault, there might be 20 volts drop in the hot wire, and 100 volts drop in the EGC, this means that anyone touching the appliance would get a 100 volt shock, which is more likely to be dangerous.
Not only is the touch voltage greater, but it will persist for longer, possibly indefinatly in extreme cases, since the reduced fault current means that the fuse takes longer to open, and in extreme cases might never open.
The other reason may be to "future proof" an installation.
Someone in future might find hot and neutral suited for 50 amps, and install a 50 amp breaker, despite the EGC being only suited for perhaps a 20 amp circuit.
The EGC could get dangerously hot before the 50 amp breaker opened.
