Downside to "revealing" system?

@dannad....exactly...none is “absolute” or “correct”...you may seek what pleases you the most, but improving one recording may seem to worsen another, so, I think, chose your favorite “references”, and work with those....

Without some details regarding what unlistenable means I can’t begin to speculate on the source of your dissatisfaction. Does UL mean worn out, excess surface noise, thin brittle sound, lack of dynamics, distortion and fidelity issues? The issue I have seen with gear that really benefits from tweaks like speaker positioning, VTA, sound treatment etc. those same systems are way below par when they are not right. Less refined systems appear to be more robust when poor setup is at play. Much like horses, Thoroughbreds won’t run if the oats aren’t hand sorted but the old cart horse just keeps pulling. No!, I am not recommending downgrading for consistency. I am just pointing out that it is way too easy to make a stellar system sound hopeless but efforts to fix it can pay off royally. Throw in some granularity on what UL means in this instance. I have lots of experience observing great gear performing at levels way below that offered by mediocre consumer grade electronics.

“Revealing,” as so many have implied here seems to be a very subjective term. I agree with D.S.  If a classic old recording sounds “unlistenable” it’s not that the system is too revealing.  Revealing should mean more detail is exposed, not that an element of distortion is present.  A system that is truly revealing should sound good in all but the very worst recordings. Classic LP’s are not in that category.

I agree with most of what is stated above.  Over the past 2 years I have built the most resolving system in my life (and I have had a few very, very good systems).  There is no doubt that for all recordings you will find differences between them.  Some are simply engineered better than others.  Some are not so well engineered.  You can also end up with an album that was pressed at the end-of-life for that particular stamper.  It does make a difference in SQ, and not a good one.  Some records of the same album are pressed at different pressing plants which can sometimes use lesser quality vinyl or make pressing runs well beyond the quantity of what that stamper was intended to do.  What was the sonic signature the mixing was intended to sound like?  A good question.  That's just one area of creating the recording that can have an effect on the SQ outcome.  And there are many other areas of consideration as well.  I personally find that even the poorer recordings are quite listenable, particularly when it is the music I am most interested in.  However, for sonic bliss and pleasure, those extremely well recorded and properly engineered albums make it all that much better.  The mastering, the plating, the pressing, and the quality of the vinyl material all make quite a grand difference in SQ.  For my present and very resolving system, and when playing those lesser SQ albums, I simply keep the volume down a bit.  That, for me, is the method of tone control rather than introducing some other device into the signal path.  And believe me, on those superb recordings, I most often enjoy them at a rather high SPL  and with a very satisfying grin.  
I have a number of albums that sounded just OK but have replaced them with bonified quality reissues.  For example, the first Dire Straits album, self titled Dire Straits, sounds good but not great.  When MoFi did a reissue of that last year using high quality vinyl, superbly mastered, and cut at 45 RPM I bought a copy.  Holy cow!  That is one fabulous sounding album.  Light years beyond my original copy.  The examples can go on and on.  I hope this helps you.  I hope that you find satisfaction.  
Do enjoy the music.

@joeyfed55 
Perhaps you may prefer the sound of adding tubes into your audio chain to take the edge off of revealing/analytical and move you more towards musical.  Tube phono preamps are a relatively inexpensive option to try such as the Pro-ject Tube Box S2 $400.  
4000 vinyl lps , I’m impressed.  Seems you are deeply into music playback.  Perhaps you should consider digital music streaming services which would greatly open up your musical selection options.  Also, if you are the vinyl cover art/info, Google CD “metadata” to see if you want to pursue.