Can a great system make a mediocre recording sound good?

My speakers are better than headphones because, among other things, headphones don't have a subwoofer.

I have to come down strongly as a no on this one. A poor recording is a poor recording. The system can't put anything there that isn't there. It is my belief that the measure of analog is analog. That is you don't really see the value of analog so much from comparing it to digital recordings as in comparing good analog recordings to poor or indifferent ones. I think this is what really makes you appreciate the artistry of producers and engineers in getting sound onto an analog medium. I recently had a general upgrade of my system that particularly improved the analog side, and it is quite the experience to listen to a record you know of old find it sounding better than it ever sounded before. But when played through the same equipment you will find that there are recordings that just fill the room and there are others that lay there like a lump. One thing I've been doing as I revisit my LP collection is listening to the English folk music I love, and I still love the music but by and large they really weren't that well recorded. On the other hand, while it may just be an effect of what's in my record library, what I've been particularly impressed with are record from the Warner/Elektra/Asylum menage, For example, Paradise and Lunch by Ry Cooder, and Swordfishtrombones by Tom Waits. Actually, one of my more unusual analog appreciation moments was listening to an old Alan Sherman record and being struck by how good it sounded.

On the digital side, I once tried something I think of as the DAC/CD Death Match, when you take an early digital recording you know to be pretty dire and run it through a good DAC to see if it can be redeemed. My match was a Denafrips Ares II vs. the extraordinarily harsh MCA Broadway Gold digitization of the original cast album of Porgy and Bess circa 1992. I'm afraid the CD won that one.

The trouble with this "it's not the system it's the room" argument is that the good recordings and the mediocre recordings are both being played in the same room. Moreover, it is the same room as my upgraded-from system. I fail to see what difference the room would make in comparing one recording to another in the same room. Judging from what some people spend on gear I'm sure some of them could afford different rooms to listen to different records, but that is not a lead I am in. A better system makes all recordings sound better than they were, but they all finish in the same order as before in terms of recording quality.

The Ry Cooder record is indeed a good choice, but I made it back in the 1970s when I bought it. Speaking of good choices, one thing I learned now that I have heard just about all of the original versions of the songs he covered, that whatever you think of him as a musician, he sure knew how to pick them. Something very interesting could be written about folk singers as music critics, based on their choice of material. 

The ultimate example of the difference digital mastering can make is a comparison of the first, second and third generations of the Complete Robert Johnson, the last of which is an absolute revelation. I think they might have had the original metal parts for that one. The ultimate test would be if someone had a pristine set of original 78s to compare it with, possibly to be found next to the Arc of the Covenant in that big warehouse at the end of the Indiana Jones movie.