Is a highly discerning system enjoyable?

I had JSE Model 2's, they measured and sounded the most accurate of any I owned. Whoopie! I drove them with McIntosh SS, 300 wpc. McIntosh SS Preamp.

After a few years, I missed my vintage speakers, extremely efficient, driven by vintage McIntosh tube preamp and more modern Cayin tube amp. They have 2 level controls each (balance mid horn to 15" woofer, balance tweeter to that result, I balance them with SPL and Test Tone CD. 

Gotta say, I prefer the vintage horns to the very accurate JSE's. My friend has those JSE's, updated them, he loves them, yet when he listens here, he finds these very involving. Involving has been my criteria once I clearly understood that factor so many years ago.

It depends.  You can have a system that lets you hear every detail on a recording and also engages you emotionally, or you can have a system that gets all the detail but none of the emotion.

I have a pair of speaker cables that I can hook up with no other changes to my system that somehow manage to filter all the music out of my music.

I think that there's a place for a receiver and sound processing to make poor recordings more enjoyable.  Whenever I've made a change that I felt was a significant change/upgrade I've found that my favorite albums and songs tend to shift a bit.  There's also an aspect of simply becoming more annoyed with poor recordings as a more critical ear is developed from listening to systems with a high SQ.

When I got my Denafrips Ares II DAC a pleasant surprise was that several of my favorite albums that are not great recordings became enjoyable again.  I guess it would be fair to describe the DAC as being "musical" in my system.

yes generally, if the system is well conceived and executed

What you need is a system that can separate the instruments, but still give you emotional enjoyment, that way you have all the details without the fatigue.