But... would that even be true?
I'm a long way from total familiarity with the lore, but aren't replicators based on the same Treknology ("Heisenberg compensators", ha-ha!) as the transporter-beam? If so, running anything through a transporter could presumably produce a (storable) record of its matter-pattern, including the radioisotopic decay-state of each individual atom, that would then allow that object to be reproduced at will in any replicator (in much the same way — but with vastly more sophistication — that 3D-printer object-templates can currently be downloaded and used). How would anyone then be able to distinguish a genuine/ original/ "valuable" work of art, e.g. Da Vinci's Mona Lisa, from a perfectly-replicated copy of it?
So there could no longer be any such thing as a unique collectible oddity or rarity, at least not once the original had been analysed — because any would-be counterfeiter wouldn't make just one copy, he'd make as many as the 'market' wanted! And without any possible means of authentication, the social cachet inherent owning such an object then simply ... disappears.
Absolutely true for the technical part
But with art for example: some artists can make close to perfect copies already of famous master works.
They can do that even better for much of the older paintings like Rembrandt or Da Vinci !
It is not only the varnish that gets more brownish over time, it is also the colors themselves that discolor over time. Da Vinci experimented a lot with that like most masters. Art was in those days to a higher degree craftmanship.
If you take the color yellow, the kind of yellow you use for lemons, on Dutch paintings in the 16th, 17th century, we do not see the splendor anymore of that color as it was when painted. But at the moment of creativity and the new owner proud on it, the color was perfect. And other colors were tuned to it, to match or contrast to it. The color affected, the composition affected.
And despite that... people want to see the original as it is when they look. Up to even the point that some museums are against replacing the old brownish varnish with new transparant varnish. As if the original is not original anymore when there is no authentic decay !
On top people love to hear something special about the creation process, some apparent flaw or oddity that makes possession or in a museum looking at it even more special.
Like for example the famous bronze statue "Perseus with the head of Medusa" made by Benveneto Cellini.
Cellini was always drinking and feasting too much in a chaotic adventurous life and had sold much of the expensive tin (bronze is tin + copper), he got for that statue, to pay his bills. The issue is that when you do not add enough tin to copper, the melt needs a higher temperature AND starts solidifying during casting, pouring the melt in your wax-gypsum mold, at a lower temperature.
During the melting Cellini had to throw all his tin tableware and cutlery in the melting pot to get something decent, but when pouring that into the mold the bronze solidified a bit too early and one of the toes is not complete.
And that is still a boring nice story compared to the many erotic-romantic stories of models, including highranking nobility etc posing secretly naked, being a mistress of an artist in between such romantics. A story becomes more than a just a story when imagination is encouraged to create your own version of more. Who was that lady of that Rubens or Picasso painting ? Did Van Gogh really killed himself the same evening he finished that painting ?
etc
Is that really the same sword that Genghis Khan used in that battle ?
Mass production, also by the process you describe, leads I think to a drive for identity and true genuine authenticity