SBJ bonds the case to the grounded conductor to create a equipotential and an inherent path back to the source. It doesn't mean the secondary side's grounded conductor is earthed by the EGC.
Of course the EGC will be connected to Earth.
You can have a gradient on the EGC from the GES to the SDS due the the wire's impedance that can result in a sustained fault and potentially risk shock, fire, or destruction of material used in the electrical installation.
So why is a GEC not subject to this impedance? And where is all this fault current flowing on the GEC coming from? The only time I see any fault current flowing on a grounding electrode conductor is from contact with medium voltage lines. That is extremely rare, and besides we were originally talking about a separately derived system which is unlikely to have contact with higher voltage lines.
The impedance on an EGC sized to the OCPD on the primary side would not be enough for the fault currents and most likely would even allow for a current divider situation that limits the fault return. Some current through the the earth, some through the piping, some returning to the utility transformer and potentially a voltage gradient between the SDS "grounded conductor" and the service's GES since some of the paths will have an impedance. Thus imbalance and poor earthing could create a difference in potential between the system's GES at the service and the neutral point at the separately derived system. Not to mention, the restriking insulation failure issue and voltage rise in ungrounded systems. Voltage stability on the secondary is important and one of the reasons we ground services.
Again there is not fault current flowing on the gec, that is not its purpose. Also I was not talking about ungrounded systems.
The SBJ would be the most important but the GES being connected would be second.
About the only thing a GES does is help clear a MV fault, like if a MV line falls on a service drop. it does reference the system grounded conductor to Earth, but I guarantee you that's going to happen anyway even without a grounding electrode system when you consider water lines, wells, things fastened to masonry, etc. (assuming all bonding is done correctly).