Regarding the precision and enjoyment, I cannot help but remember some of the content from the RMAF panel talks.
The engineer from SOny (Naotaka Tsunodo) said something about studio precision headphone bringing the listener closer to the instruments and voices, and the ones for music listening were not as close. Something along those lines, and why there is a difference for application/purpose. Which makes sense as some people want to be in the front row, and not necessarily be the microphone XD If you get too close to the instruments and voices, it's not always enjoyable (relatively speaking) .
From my experience when I am enjoying some music, and then I hear something weird (like a pop, buzz or something odd) is when I run to the can bin and grab of the "tools" to see if I can hear deeper/closer. I feel like the "tools" I generally acquire were more on the thinner side with blacker backgrounds and speed to catch any oddities so I know the "enjoyment" one is not broken / defective.
I cannot confidently say the 660 is the best "tool" out there, thought it's not bad per se. It seems more in line with the "enjoyment" side.
And sometimes the key word is "tools"
, to check different aspects (like bass, imaging, soundstage etc) which are not necessarily best to check on one paticular tool.
Perhaps why there is no one perfect holy grail for everything, perhaps there is a holy grail studio, and one for enjoyment.
YMMV