What do audiophiles want from a cable?

I try to use cabling to my advantage in the sound system.  Cables are ALL different and they have different traits and effects on components, rooms, and recordings IMO.  Key word being different lol.  No cable, system, room, speaker, ear, or brain is exactly the same really, so it seems to me that everyone's mileage with cabling will vary MWard.  What you will hear in a cable that you are using in your system, in your room and with your brain will almost always be different from another reviewer in another location, that's for sure. 

I can hear a certain cables sonic signature in my sound system.  I strategically put cabling into the system with specific components where I think they will work best in order to improve the system as a whole, and get the sound I want to hear.  It's a trail and error thing until you find what you like or what you think is most true to the source.  Spice is nice, but you have to start with a good room and good equipment or a good cable could be wasted IMHO. 

Cables are components, just as important as active components. Your question is in essence incorrect.
Can you hear anything without cables?

I think the crux of my question is, am I a good audiophile?  Am I judging cables the right way.  I'm entirely focused on accuracy but not on how they make instruments sound, does a piano sound like a piano, or would I rather have it sound like a poorly recorded piano?  What is the accepted measure?  Would you rather have a piano sound like a thin representation of a piano or would you like cables that fix that problem?  Is a cable that fixes the problem the best cable?

Well, of course, ideal cable should not alter the signal while transmitting it. But that's ideal, so any cable does alter the signal to a degree. The question is how do we want the signal to be altered since we cannot fully avoid it ?

Yes.  If the piano is recorded well and your room/equipment are capable of producing, then the piano should certainly sound like a piano.  Yes, great cables will allow a capable system that is setup correctly in a proper space to more accurately reproduce the sound of a real live piano.