*copper-age
The widespread use of copper for other purposes than jewelry has begun only after it became possible to produce in a reproducible way various alloys of coppers, now known as bronzes.
The tin bronze, i.e. the alloy of copper with tin, has been discovered relatively late, around 5500 years ago, close to the time when writing has been invented, so we have much more historical information about the civilizations that used tin bronze. (The much cheaper brass has been discovered only long after the method of iron extraction, during the Greco-Roman Antiquity.)
Nevertheless, for several thousands of years before, other copper alloys have been used, e.g. arsenical bronze or antimony bronze, so that is still "bronze age", even if it would be useful to differentiate between the ages of iron, of tin bronze and of other "bronzes". The Egyptian state definitely belongs to the age of the tin bronze.
so while you're right that copper is much less useful than bronze for most tools, here the tool we're talking about is one of the exceptions
they also tried tubular reeds, with and without water. those didn't work at all
the egyptian state seems to predate not just tin bronze or even arsenical bronze but even copper tools, at least in egypt
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† emery doesn't occur locally and doesn't start appearing in the drilled holes during the first millennium of rock drilling
Even after the much cheaper iron replaced bronze for most uses, bronze remained the best choice for a few purposes, but nonetheless that does not override the transition from the bronze age to the iron age.
While emery does not occur locally, the island of Naxos is closer to Egypt than many other places from which various goods were imported at that time, so that was not a serious obstacle against its use.
The conclusion of the parent article was that emery (with copper cylinders) produced the best matches with the archaeological artifacts, so that was the most probable method used for drilling (the other possible alternatives, like importing diamond dust or corundum dust from India have probabilities far too low to be believable; what we name now as diamonds became known to the Mediterranean world only after the expedition in India of Alexander the Great; the word "diamond" is much older, but it was previously applied to osmium-iridium alloy nuggets, which are found together with gold nuggets in alluvial deposits and which are embedded in the gold of many ancient Egyptian artifacts).
- there was a 'chalcolithic' period of copper tools in most places before the advent of bronze, but i believe that bronze tools were already in use in egypt when drilling started
- later investigations did not find emery dust in the oldest drill holes, leading to the conclusion that the abrasive was quartz, so although the egyptians certainly could have been importing abrasives from naxos, they don't seem to have done so until much later
- the identification of plato's 'adamas' with an osmium-iridium alloy is quite dubious; he was certainly talking about a metal, but it could easily have been steel or meteoric iron
- just to clarify, you probably know this, but corundum dust and emery are the same thing (the article was fairly confusing on this point)
Everything they did could be explained by mastery of use gravity, ropes, and levers. If the materials used were primarily organic in composition the tooling would be long gone by now.