Your copy doesn't just lack 'authenticity', it also lacks something uncopyable, and which is only relvant to physical artifacts: 'age'.
The fact that digital copies can be perfect, and never age or deteriorate due to the inevitable march of entropy, is a fundamental difference and yes that affects how valuable 'owning' a digital artifact is versus owning a physical one.
I think this is basically true. Impermanence is part of what makes possession important. I can totally see the value of all NFTs decaying on long time scales because they're just boring.
But on short time scales all age is similar and authenticity seems to be sufficient to at least toss a bunch of liquidity from place to place.
But you've hit on exact problem the blockchain solved from day 1, you can copy the image (just like you can download hi resolution scans of baseball cards) but the underlying "cardboard" cannot be copied, or copies can be detected with 100% accuracy (depending on how you look at it).
Some day, the last original 1986 Barry Bonds rookie baseball card will disappear, lost in a housefire or an alien invasion or something. There might still be high quality digital images of what that card looked like, in archives of eBay auction pages and the digitized records of the baseball hall of fame and whatever other ephemera wind up in the Svalbard vault.
And in fact, the photo reproduction on that card was already a poor 1980s print quality reproduction of an original photo of Barry Bonds, which probably - no matter how well it was looked after - will have suffered and faded with age as print tends to; and that actual original photo was probably reproduced in a bunch of other places outside of that run of baseball cards - and maybe the original negative of that film exists in some archive somewhere, with a high quality digital copy available - from which you could reproduce an even higher quality picture than was presented on that card.
But you would never be able to replace that card, because the point of the card was its physical connection to the moment in time where a legendary career started.
"Humans preserved this specific lump of matter and kept it safe over a long period of time even though that was difficult and, let's be honest, not very important" is what gives value to antique collectibles.
"Humans preserved the cryptographic chain of custody of this sequence of binary digits that reference a specific widely archived piece of digital media over a long period of time, by creating a distributed computing system that just automatically ensured it would be passed on to posterity whether posterity wanted it or not," doesn't create the same human connection.
The fact that digital copies can be perfect, and never age or deteriorate due to the inevitable march of entropy, is a fundamental difference and yes that affects how valuable 'owning' a digital artifact is versus owning a physical one.