Dave, can you explain - precisely - why you need to see the cable you're listening to? If the difference is heard, a blind person would pick it out.
You should also download Audio Diffmaker. Show us what your cables are doing.
If the signal doesn't change, then what is going on?
Elysian, balanced is mostly a product developed by marketing. Well, for audio. If you have to transmit signals over many miles it really does help. For 3' runs it has no value. But you sure can increase the prices and make people buy new cables.
Those preamps you saw are pure marketing. Some people sat down and decided how best to position features to extract the most profit.
And, yes, there are real problems with balanced:
1. Doubling the parts doubles the points of failure. You will have twice the failures and twice the chance of having to send it to the shop. All parts wear out and fail eventually. Further, repairs will be more costly because it is more complex and there will be more to replace.
2. Doubling the parts doubles the heat. This can be managed with bigger/multiple chassis, but a lot ofnstuff out there isn't designed for maximum cooling. It is designed (again) by marketing who put all other considerations aside so there can be a 1" thick aluminum faceplate (or whatever) because consumers associate that with "quality."
3. Not everything marketed as balanced actually is balanced. You can use a $25 input transformer so the amp will accept a XLR jack, run that through a single-ended amp, then use output transformers connected to XLR jacks. It adds maybe $100 to the build cost. Yet it will be loudly trumpeted (by marketing, again) as OMG BALANCED!!!!!! and the price increases by at least $1,000. To be fair, input transformers are good things. But not $1,000 better and single-ended amps should not be marketed as balanced.
4. Then there's component matching. Something you don't hear much about. The average layperson thinks that a 100 Ohm resistor is precisely that.
The average component comes with a tolerance, typically 10%. So a 100 Ohm resistor will be anything from 90-110 Ohms. To have a 20 Ohm variation between left and right really is a Big Deal. You'll get a channel imbalance. Better parts will have a 5%, 2% or 1% tolerance. Those are more expensive. Even then, a 1% tolerance will result in a channel imbalance.
If you want a really tight tolerance, you have to buy a lot of extra parts and hand-match them with a meter. I did this with speaker crossovers once. I had to buy about $50 of extra resistors and caps then took a couple hours to hand-match. I got left and right mirrored to .005. Excessive, but I wanted it done right. Mind you, this was with about 20 components total. If I had 200 components in a balanced amp, then I would have spent another $500-$600 for parts and spent 9-10 hours matching and sorting. In a production environment, that can add an extra $1,000 to costs.
So excessive matching doesn't really happen unless you're an obsessive DIY'er or paying high four figures for a custom build.
To get to the point, a balanced amp has twice as many parts and twice the variation in values. The chance for a channel imbalance is higher.
And speaking of channel imbalance, I always find it curious that the Golden Ears who can (supposedly) hear unmeasurable differences between cables cannot hear the channel imbalances in their amp. After all, the imbalances really are there. You can measure them. You can also go through the gear, component by component, and measure how they vary between left and right.
So if unmeasurable differences are "night and day," then a measureable difference should have its hands around your neck while jumping up and down and screaming.
Yet the Golden Ears never seem to notice that.