Why can't Trekkers use their transporter buffers to keep back-up copies of people transported?

Question

In TNG S6 Ep22, Crusher wants an autopsy to help determine whether someone was murdered, but the dead guy’s family has cultural objections. In the story she goes ahead anyway, jeopardising her career - and that’s not the point.
To me, it seems obvious that some simple combination of replicator and transporter should allow Crusher to make a copy of the corpse and autopsy that… or if you want to be awkward about it, quietly autopsy the original and offer the copy to the family for whatever ritual their culture follows.
Personally, I think the very idea that even early Trekkers couldn’t use their transporter buffers to keep back-up copies of every transported “passenger” risible, except for bandwidth or storage capacity but even that isn't the point.
Routinely buffering every transport might be unreasonable but here in S6 Ep22 it’s by no means routine… it’s next to being an emergency and if we could imagine such a replicator or transporter copy taking 10 or 100 times the normal resources, is anyone suggesting a whacking great starship couldn’t cope with that?

Michael Stachowsky · Answer

First, replicators cannot replicate living matter (at least, Starfleet replicators cannot.  source and another question with a great answer about it).  So at the very least all that doing what you are proposing would do is get you a bunch of corpses.  Now, your question does specifically ask about replicating corpses, so I suppose in that sense it would ALMOST do what you want.  Except that patterns degrade in the pattern buffers.
So, to combine the two technologies, you'd have to deal with the limitations of both.  The replicators cannot replicate matter exactly, because they do not store the data of individual molecules (see the linked SE answer).  The pattern buffers COULD hold that data, since they have to replicate the person on the transporter pad, but they can't do so indefinitely.  Thus, storing a copy of a person with the fidelity to replicate them or their corpse exactly is not within the realm of starfleet technology.

Why can't Trekkers use their transporter buffers to keep back-up copies of people transported?

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