There are a few key things left out of this analysis. But I should preface this "critique" by stating I'm a fan of digital music and no longer own a turntable or other purely analog source.
This analysis assumes that the analog source signal has no content above 20Khz. In reality, the signal will have many harmonics well above 20Khz, which have to be filtered out to prevent aliasing artifacts. This is not easy to do. Higher sample rates make it easier, but still not trivial.
A practical high-order low-pass filter will still introduce phase shifts and frequency response aberrations, and require a fair amount of circuitry (usually done with op-amps) which introduce their own distortions.
Once the signal is digitized at a high sampling rate, it's fairly straightforward to digitally filter the data and down-sample back to Redbook, but this will no longer be an "exact" copy of the original input signal.
16 bit samples are probably adequate to handle the dynamic range of the source content (particularly with all the compression that is often used), but this assumes that the full 16 bit dynamic range is utilized. In many cases the input signal is captured at well under it's maximum signal level since it is virtually impossible for the recording engineer to anticipate the maximum signal level that the musician will create.
I've talked to a number of recording engineers who say they try to set the levels based on a sound check, and then the musicians play much louder during the recording session resulting in clipping. And, of course, musicians do not like it when the recording engineer tells them they have to do it again because of a mistake they blame on the engineer. As a result, most content is captured significantly below the maximum digital signal level.
If the content is captured with 24 bit samples to start with (best case is probably closer to 20 bits of real signal-to-noise), then the recording and mastering engineers have more room to adjust levels and achieve closer to the Redbook dynamic range potential.
If everything in this process is done optimally, I think it's possible to convert to Redbook and achieve stellar results. With well-recorded and mastered content, Redbook audio can sound fabulous.
Since everything is rarely done optimally, having a little headroom in both sample rate and bit depth can be helpful.
Converting the digital back to analog can also create artifacts. If the output is not bandwidth limited, the conversion process will include high-frequency "mirrors" of the original signal. Many listeners find these artifacts fatiguing.
Most DAC manufacturers have resorted to oversampling the digital data and implementing these filters mostly in the digital domain.
So we end up sampling the input waveform at several multiples of the Redbook frequency, then downsampling to 44.1Khz to store the data. Then on playback, we end up upsampling the data back to a multiple of redbook so we can implement the reconstruction filter largely in the digital domain.
It seems logical that avoiding the down-sampling and up-sampling steps would result in a purer reconstruction of the original content.