I think acoustic timbre naturalness is first and second IMMERSIVENESS, i suppose your system is well designed enough to give you minimal clarity and the least distortion... Most well designed system are able to give us that now, with mature dac technology and amplification...
Timbre naturalness is difficult to reach but immersiveness with headphone and speakers was harder the most to reach and asked for many, many modifications and experiments and tuning... With headphone it was more difficult for me...It takes a rare hybrid headphone to reach it AKG K340 and exceed my past Speakers Mission Cyrus 181 in his acoustic dedicated room...
In this video this acoustician explain it all :
https://www.youtube.com/watch?v=4i7T1BiC-fI