You are only partially correct.....
It is true that, in the air, on the way to our ears, most sounds exist as a continuously varying level of air pressure.
However, inside our ear, our hearing works when different frequencies cause tiny hairs of different lengths to vibrate, which excite the nerves attached to them...
Imagine a long row of tiny tuning forks - each tuned to a slightly different frequency.
The process is actually rather like a mechanical spectrum analyzer... but more digital than analog in nature.
We absolutely do NOT "hear the shape of the waveform of the air pressure".
And, as far as I know, our individual nerves convey information as a series of pulses, that vary in frequency based on the amplitude of the signal.
So, as that 440 Hz sine wave gets louder, the nerve channel dedicated to that frequency delivers a series of pulses at an increasing rate (pulse frequency modulation).
By any definition I know that system would be described as being digital - and not analog.
I would also point something out about comparing analog and digital recordings ...
It is relatively simple to make digital recordings and the process is more or less real-time in nature.
As a result it is quite simple to play an analog vinyl album, make a digital recording of it, and immediately compare the two.
This makes it easy to detect even tiny differences between them.
(And tiny differences between recordings made using different equipment.)
However, the reverse is not at all true.
I would be willing to bet that nobody on this forum has ever taken a digital file, converted it into a vinyl album, and then compared the way they sound.
(Some modern technology would allow you to create a master and press an album in a few hours... but this is relatively new... and extremely expensive.)
Therefore, while you may have personal experience of how close a digital file is to the original, at least one you recorded on a moderately priced sound card or ADC....
You have NOT had the opportunity to compare a copy made on vinyl to an original to see how closely they resemble each other.
(In fact, such a comparison would be moot, because we all know that certain equalization and limiting is required to prepare a recording to be applied to vinyl.)
While some professional musicians may like the way vinyl sounds, as part of the artistic process, they pretty well all agree that a vinyl pressing does not sound like the master (and the digital version does).
However, because of the difficulty and expense of "making a vinyl recording to compare"...
What happens is that, when doing that sort of comparison, many of us have a tendency to WRONGLY treat the vinyl album as if it were some sort of original, and assume that our goal is to duplicate the way it sounds.
This may occur because we falsely assume that "all analog stuff sounds the same - at least compared to digital"...
Or it may occur simply because, as consumers, until recently, that vinyl album copy was "our de-facto original source"...
And, no, comparing the vinyl and CD versions of a certain album doesn't even come close to this goal.
Even excluding the limiting and EQ necessary to record the signal onto vinyl it is almost certain that the two are mastered differently.
In fact, even the tenth vinyl disc and the hundredth, pressed from the same stamper, will have tiny differences due to wear, and will sound slightly different.
(At least if I have two CDs, pressed from the same master, and both without errors, they will truly be identical.)
And, for that matter, it's probably not even fair to start with an analog tape master (because it already suffers from various limitations and colorations.)
The real comparison would require for us to:
- start with a pristine analog master, convert it into a high-quality digital file, then compare that digital version to the original
- start with a pristine high-resolution digital recording, copy it to vinyl, doing our best not to alter it, and compare the vinyl copy to the digital original
- see which copy is closer to being indistinguishable from the original
One final point I would make is sort of a philosophical one... and it concerns the difference between "an accurate reproduction" and "a pleasant simulation".
Compared to older recordings, modern recordings tend to be made using more microphones, located closer to the individual performers (which pick up far less room ambience), and a lot more processing.
One of the results of this is that, again compared to many older recordings, less real room ambience is included in the recording.
(In fact, with many modern recordings, the individual performers are recorded separately, without any room ambience, so the room ambience can be "designed to order" later.)
So, even when modern recordings contain a lot of seeming room ambience and reverb, it is often simulated room ambience added artificially, and doesn't always sound natural.
However, just to be clear, THE ORIGINAL AMBIENCE DOES NOT EXIST IN THE RECORDING, either because it was never recorded, or because it was deliberately attenuated or removed during the mixing process.
Playing that recording through tube gear, or making a copy on vinyl, and then playing that through a turntable, cannot replace what is no longer there.
At best, it can add some extra coloration or distortion that sounds somewhat like what you imagine was there to begin with (or that you simply find pleasing).
And, yes, at times this can deliver "a pleasant effect that produces the illusion of accuracy", but it should never be confused with true accuracy.
And, yes, in some cases the result may actually be more similar to the original.
However, since it is merely a simulation, we can never know for sure.
So, rather than "making the sound more accurate", it really amounts to "doing your own remastering to make the music sound the way you like".
Now, to be fair, there's nothing whatsoever wrong with doing this... if it's what you want.
(But, if you admit up front that this is your goal, rather than pursuing a false goal of "better accuracy", you're more likely to have it come out better... )
However, to address your "what-if"....
The problem with mechanical processes is that they are limited by mechanical precision and materials.
The current process of record production is already rather heavily optimized.
For example, vinyl is an excellent compromise between cost, wear characteristics, machining and pressing characteristics, and temperature stability.
And so, in order to make a vinyl album have significantly lower surface noise, you would have to significantly improve the overall process at many points.
(Even the best "180 gram, double speed mastered, virgin vinyl" pressings are only at best 15-20 dB quieter than the cheapest and lowest grade pressings.)
In contrast, a CD has a S/N of about 96 dB...but I can increase that past 140 dB simply by raising the bit depth from 16 bits to 24 bits...
And, while doing so would reduce the playing time of a CD from one hour to 40 minutes, it would require virtually no other changes to the technology.
And, if I wanted to, I could put 100 CDs worth of music, at CD quality, onto a single Blu-Ray disc, which is about the same size, and doesn't cost much more to produce...
(Or I could put "only" 25 CDs worth of music on that disc, with twice the resolution, and a S/N rate that was also doubled.)
And, if we're talking digital audio files, we already have the technology to put tens of thousands of CD quality tracks on a $100 hard disc that fits in your pocket.
In fact there have been a few improvements to vinyl mastering technology recently....
One is the ability to injection mold albums - which makes it practical to produce them in smaller batches.
Another is a new mastering device that produces ceramic "pressing masters" directly using a LASER.
This eliminates several steps from the mastering process, and is claimed to produce masters with better wear characteristics, and to allow more highly optimized track densities.
You get more minutes on a side, the resulting album has lower surface noise, and the master wears more slowly, so it lasts longer, and produces more consistent pressings over its useful life.
The machine itself is also claimed to be more able to comply with current environmental and safety regulations... reducing limitations on where one can be operated.
However, the improvements are still only incremental, and the machine itself is pricey...
The original sources of sound are analog in nature. The mode of propagation to our ears is analog in nature. Our hearing is analog in nature. The sad truth is that we gave up on trying to find more accurate analog means of achieving precision sound and turned to digital. It has taken many years for digital to approach in giving us an analog result that our ears truly can not differentiate from never having been anything but analog. We are close today and the other benefits of digital (storage, noise free, non contact, non wear out, etc.) have won out. But who knows where we could have gone concentrating on pure analog?