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I assume they come with a sufficient power source?
That may be the real value.
With a replicator, you can turn matter into energy, which you can turn into other matter.
There are some super rare elements, structures and materials that cannot be replicated.
These unreplicatable ones become the most valuable. Likewise, the value of original or unique sentient-being created artifacts.
Conversely, the value of things that can be replicated is effectively reduced to the energy cost, give or take transportation costs for items that can only be replicated in large industrial replicators.
Energy cost becomes the key value. Not a problem generally, but in a constrained environment like a starship at maximum warp over long periods (e.g., Voyager’s first years in the Delta Quadrant), it can require rationing of replicator usage. (Holodeck had a separate and incompatible power source.)
The most widely known example of an element that can’t be replicated is latinum, which replaced gold as a measure of value. Gold is replicatable but latinum is not.
Other examples include dilithium crystals needed to regulate warp core reactions and benamite crystals needed for the quantum slipstream drive.
Some materials that cannot be replicated in the 23rd century can be otherwise created in the 24th century. The technology progresses through time in-universe.
I believe there was a post or file at the old place that listed all the canonically identified unreplicatable materials. It might be one to bring forward to c/DaystromInstitute. @[email protected] can you weigh in please?
I think you got most of it covered except for living materials, which can’t be replicated because of the resolution limitations of replicators - like cargo transporters they operate on molecular resolution instead of the quantum resolution required for live transport. Gagh is a good example; because it ideally needs to be live it can’t be replicated in its intended serving form but has to be kept in barrels in cargo.
The other limitation would be stuff that’s prohibited by program not to be replicated, like weapons, banned substances, although that’s of course a coding issue rather than a materials issue.
Also, to correct a common misconception/inaccuracy repeated above - replicators don’t convert matter to energy or vice versa. They operate by dismantling the raw material for replication like a transporter does then reassembling them in new forms. The underlying technology is the same as the transporter, except that it rejigs the matter stream into a new configuration.
Which is why the question as to whether you want a holodeck or a replicator strikes me as a bit off because replicator technology is part of the way holodecks work. When you eat food on the holodeck it’s very likely that it’s replicated food, not a hard light illusion. Holograms of people can also either be hard light constructs or meat puppets manipulated by force fields, depending on the program and its requirements.
So if you ask me - holodeck or replicator, I’d choose holodeck because that gets me both the entertainment value and the ability to make objects and food.