That is simple enough, I guess. And it’s an interesting case against the future possibility of time travel. If we are ever able to go back in time, you can bet someone would introduce Plato to a way to make his voice last forever.
Hell, nobody’s ever checked the Library of Alexandria’s ruins for strange wax residues, I’d bet. 
There are many, many more and much, much more obvious. One example which comes to mind is the optical telegraph. The Greeks and the Romans had the necessary technology and yet, centuries went by until severl inventors developed it in the late 18th -early 19th century.
At the end of the 18th century Claude Chappe, a Frenchman, invented an optical system for communications on land. It was the first visual system of communications that permitted the transmission of true articulated messages. Rather than using fire or smoke or even flags, Chappe designed a mechanical system of movable arms which was positioned on the roof of a building so it could be seen from a distance. A central arm could be rotated to assume any number or positions and it had an articulated arm at each end which could also be set to any number of positions.
Why, for 2000 years of western civilization, didn’t occur to anyone that it was possible to devise a code which would allow the transmission of messages? All you need is a guy with a flag in each hand and a code. Ships now do it all the time. But nobody thought of it until the late 18th century.
In the first half of the 19th century Europe was covered by a network of stations for the optical telegraph but the electrical telegraph soon made it obsolete. Still, the heliograph and the semaphore retained certain importance in military and naval communications. Rudyard Kipling wrote a very funny poem about the helio called “A Code of Morals”.
My guess, re this specific subject:
There’s a “how big do we have to make it” issue involved. To reproduce sound, the solid analogs to audible sound waveforms in the atmosphere have to move along under the “needle” extremely fast if the analogs (ie, the “wiggles in the grooves”) are fairly large and spread-out–not wind-up-toy fast, but more like airplane-propeller fast. That’s a problem before steam technology, and not too practical before the electric-motored turntable or cylinder-spinner.
The alternative is to make the analogs small and delicate, as on those wax cylinders. But the smaller the wiggle, the more vulnerable it is to damage–the grooves get worn-down. (Amazing that we now have a generation with no concept of why a recording medium would “wear out.”) Furthermore, just how do you amplify that tiny, tinny sound output? (Edison’s answer: a big ear trumpet.)
Still, Tom Jefferson was a clever guy, and it may just be that Sally Hemings’ voice is inscribed somewhere in Monticello.
As they say, though, it’s less important to be the first to invent something…
than to be the last.
Adding to sailor’s post regarding “late” inventions…
I once read that photography is a classic example of this. All the pieces – lenses/pinholes, light sensitive salts, dark boxes – existed decades (centuries?) before someone thought to put them all together.
[DMark, who told you about my pinto bean transporter?]
Well, what if the Romans (for example) did have something similar to an early phonograph? You certainly wouldn’t expect it to have survived intact for 2000 years. The problem with that conjecture, of course, is that there’s really no contextual archaeological evidence that suggests anyone could record and play back sound before the 19th century.
On the other hand, no one would have suspected that the ancient Greeks could have actually constructed something as complex as the Antikythera Mechanism, had it not been rediscovered. From that link: