Yes, cables are definitely a vey important element of MY system. They can make or break a system in my opinion, and so can anti-vibration platforms, power conditioners, and so on. You really don't need to have golden ears to hear what they do - in my system. I've enjoyed a tremendous (yes, TREMENDOUS) upgrade of resolution, openness, pace of said system after replacing the whole cable loom. It certainly brings as much an improvement as changing the amplifier(s) for more expensive ones, or the DAC. And it costs less. It seems to me a lot of audiophiles just go through an awful lot of component swaps without ever trying to get the best out of them, wasting time and money, when very often all that was needed is a little attention to surrounding devices and cables.
Now of course there are systems where the improvements might be more subdued, and where you mIGHT need more concentration to hear the differences, which may seem too subtle at first.
Try it with a high sensitivity, fully horn loaded system like mine, and you'll be shocked. My explanation for that, is when you use 100dB+ sensitive speakers, at normal domestic listening SPLs, the signal travelling through your devices stays really really low, uncomfortably close to the plane where distortions and noise induced by external perturbations (spurious vibrations, EMI, RF, mains noise...) reside. That doesn't make it a "better" system, it's just a characteristic of very high efficiency, and is more often than not a plague rather than a blessing. Yes, in my system, you clearly hear everything, from the type of cable used to the platform where the DAC and the transport reside. It's absolutely not "subtle", rather dramatic in fact.
That being said, even in a conventional system cables are important and yes, I believe ears can be trained for critical listening, there is absolutely no doubt about that.