I don't think we understand and/or can measure pleasant distortions well enough to reproduce them accurately. Assuming one even believes they exist... for example copper cables offer lots of pleasant distortion vs something neutral like UPOCC silver, but many would dispute such differences are real and measuring this may not be possible. Paper coned drivers can make acoustic instruments sound more real vs other materials that produce lower distortion, but this phenomenon is similarly difficult to define given our incomplete knowledge of audio.
The other issue with distortion is it reduces resolution by masking fine details, in a good system this is not a positive. In a system that has unpleasant distortion like harshness, grain, etc, pleasant distortion generally sounds better as it masks the unpleasant distortions. But you end up with a system that is much less resolving and thus less engaging. Given enough experience people generally prefer a more accurate and resolving system as long as it does not produce unpleasant distortion that leads to listening fatigue. So, IMO we should concentrate on eliminating unpleasant distortion rather than adding pleasant distortion as a band-aid.