You are correct that acquiring gold for savings and selling it again later would be easier if gold was the standard of exchange as even your neighbor would have some - HOWEVER as I outline later in my post it does not make sense for gold to be the standard because it is a hassle to use gold every day.
You can't use this as an argument because you could use the same argument against dollars. It is a hassle to use cash every day. Gold is no worse than fiat in this case.
Even if gold was reintroduced we would still need government "Coinage" and banks (for digital payments) to allow easy everyday use. The banks are fiat all over again and the government coins would probably be diluted, as history has shown, which brings you back to just fiat OR miserably carving gold at the cashier.
You simply don't understand the meaning of the word "fiat". Please look it up.
The simple truth, Occam's razor, is that gold is bad money hence it is not used as money anymore.
If gold is so great, but just held back only by governments then why isn't the national currency of the Cayman islands or Las Vegas?
Gold is no longer used because governments are incapable of sound fiscal management. At the time, it was a simple choice of defaulting or dumping the gold standard. The best choice would have been to default, but governments chose to follow the long-standing tradition of fiscal irresponsibility and dump the gold standard instead.