The What If Files. A Real What?

For something to have value, it needs to be appropriately constrained by supply and demand. Specifically, you want low supply, and high demand. This is a bedrock attitude of humans that has been with us since before history began, and will likely remain with us, whatever our technological level.

So, where will coins generally, and modern mass-produced Chinese-made counterfeits more specifically, lie on the supply-demand plot in 500 years time?

Assuming there isn't a severe technological dark age or counter-technology revolution, then it's safe to say that coins themselves, as a functioning tool of the economy, will have ceased to exist by then. Nobody will be using coins for money. They will have been relegated to the same corner of the "obsolete artifacts museum" as olive oil lamps and swords: items that may be of interest to a few students of arcane history, but outside of the experience or knowledge of everyday people.

When this happens, there won't be a groundswell of "people interested in coins". Coin collectors will become a far smaller percentage of the population than they are now. This can only result in a general reduction in demand for coins. The number of specialist collectors - in this case, people interested in collecting fake coins - will decline even further, as "coin collecting" in and of itself will become a speciality. So demand for 21st century fake coins will be even lower.

The one thing that may mitigate against this decline in demand will be space travel. If humans colonize space, to the extent that a significant proportion of the population are born, live and die far away from Earth, then "Earth artifacts" will become a significant export of the homeworld. And coins make excellent "Earth artifacts" for space-dwellers or colonists of remote planets: they are small, require minimal protection from space travel and are steeped in historic importance. Now, I don't think humans will be founding an interstellar empire within 500 years, but you never know. "Star Trek" is set less than 500 years into the future.

Now, for the supply side. While genuine coins may be limited in supply, the fakes are currently not. They're being mass-produced and imported into Western countries by the shipping-containerload. Right now, for many of the coin types popular with the fake-makers, the number of fakes of that particular coin type is vastly higher than the number of actual genuine examples of that coin, and this trend can only continue. The only thing countering this supply equation is survivability - genuine coins, being usually made of stable high-quality alloys, are likely to still be around in 500 years time. The fake coins are often made of trashy alloys that will probably corrode into ugly messes within 100 years.

Conclusion: your fake coins will be worth mush less, proportionally, than genuine coins.

One good thing about coin collecting in that far future time is that hopefully by then they'll have invented a "Star Trek" tricorder-like device that they can simply point at a coin, and it will not only instantly identify it, but be able to tell them exactly what it's made of and whether it's genuine or fake. So your descendants aren't going to be able to fool themselves or anybody else into thinking their illustrious ancestor owned actual genuine coins.

So at some point all of us collectors could gather their collections to one place/location and create a massive museum of world coinage.

Ancient coins have been out of circulation for hundreds of years, but still have a following. I would think that the supply and demand are both lower than for coins of the last couple hundred years, though.
Maybe coin collecting will not go away in 500 years, but will continue a steady decline in popularity, such that the values for today's high value coins will also likely experience a relative decline. And the decline will be a bit steeper if there are not coins in use at that time.Of course, with our future having so many potential scenarios (consider how much has changed in just the last 50 years), it's difficult to guess what life will be like and how that will influence the use of coins as a medium of exchange.

It seems we are already near that point in some cases, oriole. If technology continues to advance, I'd say it is a near certainty that differentiation will be extremely difficult, unless someone comes up with a way to analyze a coin for when it was pressed so that you can date when it was manufactured.

Replicators will eliminate want and need...

"A lot has changed in the past three hundred years. People are no longer obsessed with the accumulation of things. We've eliminated hunger, want, the need for possessions. We've grown out of our infancy."
- Jean-Luc Picard

"The acquisition of wealth is no longer the driving force of our lives. We work to better ourselves and the rest of humanity."
- Jean-Luc Picard