So how can a great system solve less than great recordings

jumia;

"It seems no matter how good a system is, the quality of recording quality takes priority".  

"Good" according to whom???? 

You can assume that the more resolving your system, the more it will reveal the differences between recordings and highlight both the good and the bad. 

You are the one who is going to be listening to your system and only you know which music is most important to you. There's little point in assembling a system that sounds sublime for genres you don't care about but is disappointing when it comes to what you really love. 

For example, I've found that DACs vary enormously in this regard.Some are so resolving that all sense of the "forest" is lost because each "tree" is artificially hyped. . .never mind each tree--  more like every vein on every  leaf!  A lot of people seem to really like this effect. I'm not one of them. Maybe you do, but if not, there are other ways to go. That's the double-edged sword of this  obsession... er, I meant, "hobby"-- there's a lot of gear to choose from. 

There are also trends in recording. In the 80's, it was "cool" to make drums sound like trash cans being pounded inside a cement bunker. 
Good luck making those sound good. Or maybe you like that... if so, I don't mean to insult you-- this was merely the first example that popped into my head. The fact is, whatever your tastes, you are bound to encounter CDs that do not please your ears, for one reason or another. Finally, "remastering" is not necessarily an improvement. Check out the Steve Hoffman Forums for discussion on the relative merits of different versions of any given CD. 

Short answer. No.

Whatever you put into the system, will come out the other end with with wonderful clarity. Worts and all will be presented in their full glory. The better the system, the more obvious the shortcomings of the material is. 
Put a cell phone in the bathtub (dry tub preferred), play some different tracks. Close the door and stand outside.  It will all sound equally crappy… 

OP. I'm going to disagree with you. I say that you know your system is great when mediocre recording sound "good" and great recordings sound great. I had a Krell KPS20i way back when. The system it was connected to was so good most CD's (not bootlegs of course) sounded at the very least enjoyable. I remember The Turtles sounding like I was in the studio with them. I no longer have any of those components. The Turtles haven't sounded the same since. Joe

Nothing to do with "great systems", but I have a double pole, double throw switch to bypass my sub crossover.  This allows a lot of harmonics to be added to make up for how horrible many old LP's sound.

To help old Millercarbonfootprint understand my point, I think a great system helps everything you run through it...if a recording is simply poorly done, it still is given its best shot and being made aware of the issues with a recording is an important thing. Get it? You do...good boy!