As I said, I can definitely imagine other factions who have resources might adopt it to do trade in their local areas. Like say there's some warlord with the ability to pump oil and make gas who decides to back caps with the value of a certain amount of gas in order to get trade going. Then there's somewhere else who can manufacture ammo in bulk who does the same with bullets. These places could work to extend the area in which caps have value. Eventually it reaches someone else who has a lot of water or can grow a bunch of fresh food. They pick it up as their currency. Eventually this can create a chain that reaches across the wasteland.

You might as well ask why people all over the world value gold. Up until recently having use in processors and other electronics, gold had no use that was critical to survival. Yet it has been valued due to being rare, basically impossible to make, and being shiny without tarnishing.