Gold has no value. None. Past being a shiny metal of relative rarity, it's useless. It can be used for conductivity, but there are better and cheaper metals for it.
Gold tends to always be a reserve currency which people fall back on in hard times. People keep investing in it, in order to hedge against inflation and currency crises, because gold
always has value to people. If the Dollar breaks down, it's likely that stores will prefer to trade in gold and silver instead.
In any case, I did a little bit of research. The Fallout Wiki says the following, which makes perfect sense:
NCR's gold-backed money has lost value after the Brotherhood of Steel ambushed and destroyed their gold deposits, so NCR's dollar is now backed by water.