So, instead of tracking the physical copies -- which I think we'd both agree are an irrelevant artifact of an antiquated distribution system -- I think we should talk about the value that is created for humanity when someone comes up with a new piece of information. When I make a movie, I've added a certain amount of value to the world. When I establish that a molecule can safely be used to treat a disease, I've added a certain amount of value to the world. It is hard to find units to measure this value (revenue potential in USD is a distorted one), but it is undoubtedly finite, and different for each movie or drug. None of this changes with your sci-fi replicator.
The question is, should I as the creator of the information be able to capture all that value? Some of that value? None of that value?
If we thought of IP as a natural right, we'd say "all." Copyright would be perpetual and there'd be no fair use. In a post-scarcity world where everyone got food and housing and paint and movie cameras for free, we might say "none" and hope (correctly I think) that people would still create for the pleasure of creation.
Historically in the US we've said "some," nominally because we think it maximizes the rate of production of value for the commons, but in fact because of the natural vulnerability of our legislative system to capture by rent-seeking copyright aggregators. It is like a resonant frequency of democratic capitalism.