What do audiophiles want from a cable?

Cables essentially are tone controls. You are basically altering the lows, mids, and highs by trial and error. It just comes down to which one floats your boat in your room with your setup.

Waxwaves, you use Purist cables, all Ferox. Have you ever tried Purist fluid cables? Now when it comes to Purist it's a fun game, there used to be fluid and Ferox cables with both Ag/Cu/Au alloy conductors, that's, mostly silver, and Cu/Ag/Au alloy, that's, mostly copper. The newest Luminist revision has no Ag/Cu/Au with fluid combination.
I have original Colossus fluid speaker cables, Neptune Luminist Single Crystal Copper fluid RCAs, original Colossus Ferox RCAs, used to be fluid that I bought with Ferox, and original Maximus Ferox RCAs that used to be fluid in my set-up. Fluid and Ferox have their strengths, the analogy could be that fluid Purist, especially all copper, sounds like a tube amp, and Ferox like hybrid/warmer transistor. The Neptune that I recently got has an incredible deep and layered soundstage that I doubt  any other Purist cable could match, and also exquisite slightly rounded highs. Other things being equal, Ferox may be a little quiter with tighter bass. So, no wonder that a number of people use both fluid and Ferox cables in their systems. Some would call it sound manipulation, yet others would call it fine tuning. I would not run all Ferox cables in my system but I could run all fluid cables, provided I had Ag/Cu/Au speaker cables. Single Crystal Silver with Ferox might give the ultimate resolution speed and bass and balance with great soundstage but it costs a fortune.

I also tend to see the system in a holistic angel like renolds 853 and waxwaves. Overall i see the software, hardware, the room and finaly ouer body ( mostly the ears) as all connected to the expirience. I too have expirienced a cable the has huge synergi in one system and very little in another. When i alter a component in the system, it creates a domino effect so some of the other components in the system again can be optimised. Getting better a better and better system makes the diffrences when changeing anything more and more audibel. I whish that i could find a cheap cable that did it all right but i have never found it yet.
At a certain level i didnt need the filtercabels that takes out nasty things. Before that i hadent been dealing so much with the room, decoupling and the electric supply. For me cabels are components, i have never heard a highperformance SOTA system without superb expensive cabels. I tend to think that the powercabels today is the most importaint cable in my system and in the low level time it was the most unimportaint.

My cables, as well as the rest, shall improve the realism, make it more involving and letting me feel more when i listen to the music. I think most will go for that but how much you are willing to offer on them.
Here i am looking for the lowers fruits first and i get a lot of help form other expirienced audiophiles. When i think i have reached a homogenic level in the whole chain, i usually start lifting one component up the ladder again and then the rest follows over the years. Which component it is, depends on many things but feeling that making a good deal, eg superb price/performance matters a lot. 
Trying new super cabels in my system is a easy way to learn more of the capacity/potential in my system, that may be hidden for me. Unluckily i dont have so many opotunities to do it,as supercabels are rare in this area. Maybee we could swift cabels with each other once in a while.
Good lisining.

What do audiophiles want from a cable?  For it to sound audibly different from the ones they have! LOL!

Cable discussions and evaluations are entirely subjective ( all rooms, components and listeners are variables).  When you measure one set of cables against another ( in itself a challenge -- as meaningful blind A/B tests are almost impossible without manually switching them back and forth -- losing the ability of a quick A/B with the time lapse) -

But the question of having the cable be neutral - and not adding or taking anything away --- how is that even possible to measure or determine ?  What is your base reference for measurement ? -- It has to be another set of cables ----- so how do you know what your base reference of neutrality actually is ? --

Simple fact -- You can't listen to any of the components without cables -- So all cables must impart a sonic signature of some sort -- and it becomes completely subjective as to what you consider to be neutral.

I have spent a considerable amount of money on cables - mostly motivated by a hope that it will provide better sound staging, possibly broader frequency range and an enjoyable / pleasant tonal representation ( not likely better - just different and more personally preferred in my room/system/ears -- which may change after 6 months if/when I try another pair) --

But some moves have been in hopes of getting rid of any background noise and trying to achieve that completely quiet 'Black" background in my system ----  I find that most "good" cables do this better than mediocre or cheap ones.  I do believe that good cables are an important component -- but beyond getting rid of any background noise, hum etc.  and being dead quiet (as if the system was off when paused) -- the results are completely a matter of tonal preference -- but I can't ever say neutral -- and not adding or taking anything away -- because all you can do is measure one set against another -- what is being added -- or what is being taken away -- means nothing other than the two sets have different tonal signatures -- so it comes down to personal preference.