So how can a great system solve less than great recordings

One can only put so much lipstick on a pig.

If you've great equipment, it will only make an old recording....sound really bad really well. *L*

I can eq only so far, process to a certain degree, but....

In the end...what one starts with is what one gets to listen to. *sigh*
Beyond that, one is at the mercy of 'remastering', and all that.
"They" have the really nice toys to knock the dust off of what was once what we recall.....and we all should remember how fallible memory can be, and how it be disappointed so easily when one revisits the past. ;)

MHO....you're free to have your own. 

Forward....into the past, J

Sometimes it's that old 60's Dansette record player that gets the best out of a recording because it doesn't faithfully reproduce everything. Also if you are of a certain age, that's how you remember hearing it :^)

Why do you imagine a great system can make a poor recording better??

A great system reproduces accurately what is in the groove/pits, that's all.

If you want to go that way, get some new-fangled digital enhancer that makes the recording sound more like what you want to dial in.
And kills the soul of the music.

My goal for a system is accuracy.  If the original recording source was poor, I prefer the system that reveals that.
if I want a system that buries that under a pile of distortion and artifact, I would go back into vinyl 

Some of my best recordings are from the 50’s, 60’s, and 70’s. They knew how to record and master back then, today it is mostly a lost art and most remasters suck in my opinion. So, in answering the question in regards to making old recordings sound better, they already do sound better! Let's take Nancy Sinatra's LP County My Way for instance....I do not think it can be bettered....it sounds simply gorgeous on my system.