Should a good system sound bad with bad recording?

The problem with "a good system" is "What actually makes a system good"
And that is different in different folks minds.
So I would say the average 'Audiophile' wants a "true to life system" which will just allow whatever is in the recording to come out, irreguardless of the bad sound.
Others want a system which allows the greatness to show on good recordings, AND creates a euphonic "improvement" in poor recordings.
This is certainly achievable.. and would be preferrable to "absolute fidelity" to the recorded material.
So you can actually listen to stuff... and not just those 50 or so "audiophile" recordings.

Yes. Case in point...Robin Trowers' Bridge of Sighs, one of the greatest rock albums known to man, IMO, is absolutely un-F'ing listenable on a high-rez rig.

one solution is to have some sort of euphonic sounding component in the tape loop. click it in when to sound is terrible, and off for the great recurdings.
(And I wonder if this original post is showing why some folks rave about how great some cheap, junk system.. sounds better than their $80,000. rig.)
Is Euphonic sound for bad recordings more important than truth in sound.

if your speaking of the legal so-called bootleg, commercially released, live pearl jam recordings, the answer is THE BETTER THE SYSTEM, THE BETTER THEY SOUND. they were intentionally left ruff around the edges, but were indeed made for quality hi fi playback. aside from female voclas and small chamber recordings, most hi end systems are put through a reality check with large orchestra, and live rock and roll. most fail........are they audiophile quality...of course not....but are they worth owning and playing...you betcha

I am not sure the issue breaks down as simply as "realistic and accurate" versus "euphonic." I think your system has to do PRAT well to be consistently enjoyable across the musical and recording quality spectrums. There are a lot of other factors, including the voicing of the speakers. But I am still trying to figure out all the issues and the right balance between them.