Is it the recording that is the work of art or is it the performance that it captures (be it acoustic or digital)? If I buy a print of a painting, is it the print itself that is the art or is the art in the image that it portrays to my retina?
The "input signal" is an amalgamation of vibrations on microphone diaphragms, electrical currents from instruments plugged straight into the mixing desk, direct digital synthesis, and analog or digital processing of these signals. The recording is not music. It is merely one component in the remote conveyance of music to your ears. The art ended the moment it was recorded. Since only one component of that original chain, the microphone diaphragms, captures the movement of air caused by sound waves in the studio, and there is a whole mountain of other things on top of that component that alter the signal, to claim that the air movements caused by your speakers are somehow more or less accurate to the sound waves moving the air in the studio is nonsense.
And then, by the way, the recording first takes a trip to the mastering engineer, whose job isn't to make sure that the recording "stays true" to the sound in the studio, in which case they would just do nothing. Instead the mastering engineer alters the recording further to ensure that it will sound "good" on as wide of a variety of systems as possible.
So your quest to achieve perfection is quixotic at best because there is no standard by which "perfection" can possibly be measured. Low distortion of your components cannot account for all the other alterations that happened along the way. Nor can it account for distortions caused by your room, the shape of your head, the shape of your ears, the state of your ear canals, etc. Better to accept that distortion will happen and use it to your advantage to shape the sound so that it is most pleasing to you. If that means near 0 distortion in your DAC, fine, but keep in mind that that is merely your objective, not the objective.
