I agree that there are problems to be overcome with the analog playback system, and also the recording of records.
My take on this is that at least the analog system has the continuous waveforms recorded into it and can attempt to play them back, and the difficulties in this task are largely in the realm of the playback system to extract from the grooves. If the TT/arm/cart are up to it, almost all of the information can be brought into the system, albeit with some distortion caused by the recording process, and some caused by the playback system.
With the digital system, the sampling process is, by definition, not continuous, and as a result only a portion of the actual music is even recorded. So the many of the significant problems with digital actually occur at the master recording stage and the redbook conversion, with certain amounts of the music being left on the floor during the sampling process. Once this occurs the music is limited at that level, and cannot be recovered. So, even a top-quality esoteric digital player that makes a near perfect reproduction of the master is limited in information by the recording itself.
Maybe some feel that the Nyquist theory is valid and this is not an issue. In the gross sense, I think the Nyquist theory is valid. But not in the ultimate sense. There is a point where analog recordings can exceed the informational transfer of digital recordings, provided the analog recording is decent enough to begin with, and the analog playback equipment is decent enough to extract more information from the record than a digital recording can make. It is at this point(and above) where the analog medium begins to show its stuff. This is why people make the move to analog gear. If there was no difference, they wouldn't do it, because digital is clearly more convenient and more accessible in every way.
So, analog with all its warts(and there are many) can still provide a higher degree of music information transfer into the audio system than digital can. At the lower, more mass market levels, this may not be obvious because the analog gear is not precision enough to show the difference. At the higher levels, it is clearly obvious. I recently had a discussion with a person who has a listening buddy who has had some of the finest digital gear in existence, price no object. He currently has the latest Meitner gear, which is really, really good. He also has a very fine turntable(that cost about half what the Meitner digital gear did). The turntable exceeds the Meitner gear, and all of the other digital gear.
This could not be so, if the digital stuff fully captured the recording, and that is why I state that the digital recording processes are the limiting factor. I am fully aware that the digital stuff has a theoretical dynamic range advantage. I am aware that the background noise can be less with digital. I am aware of the "lossless" conversions concept. I know about the Nyquist theory. I know that digital has all kinds of advantages at the consumer end. And I accept all of that. But the bottom line is that it is limited by the very sampling technology that makes digital possible in the first place. It does not record the full waveforms. And when you reach the higher levels of performance, the advantages of analog(in music information transfer) show themselves.
So, what does this have to do with the main topic at hand. Just this: that the limitations of digital are primarily in the recording stage, and the limitations of analog are primarily in the playback stage. To refer back to the original question, I submit that the digital master will be more limited by the recording, the result will be that the advantages of analog playback will not be as well able to show themselves, compared to using an analog master. Therefore the differences between the CD and the LP from a digital master will be less distinct.
I know that this may be somewhat controversial, but I'm sticking to it.