I explained the Bottle Cap currency to my Sister, though I don't think she got it. It's not the caps themselves that are valuable, but you can exchange them for a glass of water from the Merchants in the NCR. The Caps are simply used because they cannot be made anymore, thus a hedge against inflation.
While Gold and Silver would remain valuable, for the average person, should Society go down this path, Chicken's, Chicken Eggs, Ammo, Neosporin, WATER. All the things we throw away or overlook will become the most precious commodity.
The game gives the player leeway to make hard decisions that will either gain or reduce your standing to other AI players in the game.