Reproducing audio quite accurately is possible. However, it requires two extremely unconvenient things :
-Being in an anechoic room.
-Having a listening position fixed with an accuracy better than one centimeter.
I've read somewhere than in a usual listening room, 70 % of the acoustic intensity comes from wall reflexions, and 30 % only in straight line from the speakers.
This is consistent with a stunning experiment that anyone with an average microphone can do.
First, set the microphone just in front of the speaker. Something like 20 cm away (10"). Play some music while the microphone is recording. The recording quality has no importance. You can record with a laptop. The microphone should be better than the one coming with cheap soundcards, though.
Listen to the result through you hifi. According to the speakers and microphone quality, it usually sounds quite bad.
Now, set the microphone at your usual listening position, record again, and listen to the result...
Usually, the result is so unbelievably bad, so incredibly different from the previous, that the only sensible conclusion is that the microphone was broken, or just good for a telephone. That's why the first recording, in front of the speakers, is necessary, in order to get a comparison.
The difference between the two is just the sound of your room ! This sound is completely corrected, unconciously, by our brain. We need a microphone in order to record it and listen to it (in the room again).
This was an eye-opening experiment for me. The 70/30 figure for the room/speakers influence looks then perfectly sensible.
Back to the topic, there is something that can't be corrected in a room, from an accuracy point of view : the reverberation.
When a speaker plays a transient sound, like a drum hit, it bounces on the walls and we hear it several times, nearly at the same time, instead of one time. No equalizer can correct this and make us hear only one hit from our listening position.
The other main parameter, resonant frequencies, can be equalized, but it is so much sensitive to the positions of the speakers and of the listener in the room, that it only works for one very accurate listening position. Just lay back in your armchair, and you need to calibrate the equalizer again for this different position !
These are the main reasons that prevent sound accuracy on a stereo system.
There are other factors, more complicated, but very interesting. The stereo imaging is one.
From the phase point of view, one first problem is that sounds coming from the right speaker hit the right ear first, and the left ear immediately after, with a small delay. The original acoustic sound did not necessarily have this behaviour. This may be partially corrected with digital processors, using phase cancellation. But room reverberation limits the efficiency of this method. And it also requires a perfectly fixed listening position.
From the amplitude point of view, the wave front hits our ear from a given direction, which causes characteristics attenuation in the spectrum transmitted in our ear canal, called "combing". Our brain can identify a given comb pattern and find the original direction of the wave front that produced it. This is a limitation that is practically impossible to overcome with headphones, except by rotating the diaphragm, like on the AKG K-1000.
These factors have led to the usual equilateral stereo configuration. Speakers must be in front of the listener, like performers were supposed to be. This is an artificial way of recreating a standard stereo imaging, not necessarily similar to the original one. For example if you listen to the recording of a street parade, with instruments playing completely to the left, and some completely to the right.
In conclusion, scientific measurments about sound fidelity are more often seen for room optimisation and speaker equalisation. The fidelity of CD players and amplifiers to the original signal is so accurate, in comparison, that measuring and adjusting them would be a waste of efforts.