"A speaker that will not let you hear a bad recording is a poor investment."
It's all a question of degree. I've had systems in my house on which about 10% of the CDs I played sounded great. The rest ranged from tolerable to "run screaming from the room" intolerable. Some would have considered those systems to be wonderfully accurate. From my point of view, they stank. And they're gone from my house, and I am thrilled.
The system I've built now will certainly let me know if I'm dealing with problematic source material. (And I think it is much more appropriate to call it "problem source material" than "a bad recording". What sounds "bad" on one system may well have sounded great to the recording engineer as he was playing it back perhaps as long as 30-40 years ago.) But it is rarely "in your face" about it. I can usually hear the music beyond the sonic problems. That, to me, is a sign of a very well designed system/speakers/whatever.
When I audition equipment at a dealer's, I always take some CDs to play that have problematic sound (in addition to some that sound great on almost anything). That way, I hear the strengths of the equipment, but I am also well aware of whatever fatigue factor exists in the equipment.
A system that is fatiguing to listen to is pretty darn worthless, seems to me. And it is hugely fatiguing to be regularly reminded of all the flaws in the source material you want to hear.
