[burnt-resistor]

That's an extreme edge-case and a strawman. Anyone operating temporary equipment on a generator during a severe storm will obviously unplug sensitive stuff to not take unnecessary chances regardless of safety precautions already in place.

Ground rods are required in certain situations according to the NEC.

Ground rods are for lightning protection, transient surges (over voltage), and induced surges; not for short protection, ground faults, or making ordinary extension cord use of bonded generators "safer".

Typically, they're required whenever it's a system that powers a building on its own, i.e., off-grid setup or with a floating neutral generator connected via a switched neutral transfer switch.

[jcalvinowens]

You can unplug everything and open all the switches, but a nearby lightning strike will still fry your generator through that unbounded ground rod. Lightning ground potential is very eager to take the shortcut to your other ground rods through a few millimeters of insulation and open switches on the path through your generator and house wiring, when the alternative might be tens of meters of dirt :)

I don't care what the NEC doesn't say, NFPA 780 says you have to bond all ground rods.