Take a deep breath and start again this thread is about is not about hair dryers or pools.
It is very simple, an inspector incorrect believes a GFCI needs a EGC to operate.
It does not. Stop questioning that, it is a fact.
The thread is about replacing two wire receptacles in older existing installations that do not have an EGC at the box.
The NEC provides options for that.
1) Replace the two wire receptacle with a new two wire receptacle.
(Seems like a fine idea, now go try to find a new, tamper resistant two wire receptacle for sale)
2) Replace the two wire receptacle with a three wire receptacle and provide GFCI protection for it.
Those are also facts, those are allowed, NEC compliant options.
This thread is not about what any of us thinks is 'better' I think we all can agree it would be better to have an EGC at every outlet box but the fact is there are millions of existing installations that do not have an EGC and the NEC can't and should not require a circuit rewire to fix a worn out receptacle.