So how can a great system solve less than great recordings

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!

For my analog only system, by getting more out of the groves, each upgrade improves my enjoyment. Surely, even unlistenable LPs prior sound good now and, yes, good recordings sound even better.
This is the case for front end and other upgrades.