From a slightly different viewpoint, in most of the LP v. Digital comparisons one reads, they are comparing a commercial LP against the CD version, or perhaps a download or stream. Particularly with classic rock material, the two releases are often decades apart and few have any clue as to what differences there were in mixing and mastering.
My view is based on my own conversion of hundreds of LPs in my personal collection to digital over a ten or more year period. That meant I knew exactly where the digital file came from. My experience is that those digital conversions sounded just like the vinyl. As others noted above, the process of making LPs involves a LOT of mechanical steps, each adding its own flavor. I've also been lucky to hear some open reel tapes over the years direct from recording studios, and they have a flavor that is different than the LPs made from them. When I converted a few of these open reel that were direct copies from the studio tape, I again found that the digital copy captured the tape's qualities.
In my mind, most of the complaints I hear about digital have more to do with the intentional choices made in the production of the CD or digital file than any inherent incapability of the digital format itself.