Monty is actually wrong, and makes a lot of assumptions about digital filters and linearity at very low levels being perfect. I did a lot of audio recording at various sample rates, 16 and 24 bit. They were all different, and none actually was capable of sounding identical to the source tape. DSD 128 was very close, though.
If you think in terms of the waveform, you are getting a continuous output that is smoothed by the filter. The irony is that many audiophiles prefer the stair steps and aliasing that comes with NOS filters like in Yggdrasil, Audio Note DACs, Aries Cerat, TotalDAC etc. This (and also DSD) actually points to the problem being the filters themselves required to reconstruct the audio. I've yet to hear a DAC that could sound as continuous as an analog source, and it does always seem somewhat like an atomized approximation, if a very good one. Who knows why.
Current crop of top DACs are probably pushing the limit of what a DAC can do with a digital recording, but they don't have control of the ADCs involved in the recording, and there seem to be some limits in terms of ultra-fine timing response with PCM filter design and bandwidth. At this point many things have been tried: higher sample rates, DSD, DSD upsampling, NOS filters, adaptive filters, apodizing filters, MQA. All help in some respects, and some are detrimental in others. But nobody has fully cracked the problem of getting the analog playback quality without some kind of performance compromise.
Still, we are at a place with satisfyingly musical and extremely high performance digital, so I don't lose sleep over it.
(BTW, my reference points are source tapes. Vinyl definitely adds a sound, and its own rhythmic quality. Maybe adding that sound is enough to satisfy many. But I'm just looking at whether and how digital mediums can perfectly reproduce tape or live microphone feeds, and there is one hard to describe dimension that seemingly nobody has mastered yet.)