> I think you'd find that producing convincing imitation U.S. bank notes or even coins is considerably more difficult
No, actually. The dollar is really quite different than gold or silver.
This is because even after the "american empire" falls, there would still absolutely be people with the ability to replicate dollars very easily, and who would also be willing to do so.
That entity would be whoever owns those US dollar printing presses that are printing the dollars right now.
If the US is in a state of collapse, but people are apparently still accepting US dollars in payment, then there would be a strong incentive for who ever controls those already existing printing presses, to produce more green pieces of paper, and exchange them for goods and services.
The same is not true for good and silver.