I'll hop in quick to say that if we go believing that DACs sound the same despite measurements, and we go find the most likely explanation, psychoacoustic properties are maybe a million times more plausible than "rare undiscovered measurement" or whatever. Just the fact that our long-term memory is garbage, the fact that we can percieve sound differently when rested and tired, the fact that different volumes have different psychoacoustic curves, the fact that placebo exists and is very, very strong, the fact that we listen more intently when we get new gear or compare intently, all of these are a billion times more plausible to me than some magic DAC element that by the way, engineers also don't know about so you're suggesting that we just design gear blindly and put a bunch of shit in there and maybe it'll sound good. Why not go further, do two DACs of the same model sound the same? If I buy a Modius today and a month later, which one sounds better? Sure the measurements won't show it, but....etc, etc. That's why we need a test that elminates this variable, and it's the ABX test. As humans we often first question anything but ourselves, it happens to everyone. Ask a producer if they hear the same thing if they start on a mix in the morning and mix all day to the evening. Ask them if they ever thought that something they changed produced a great change that fixed the mix only to discover they had the bypass on and the effect didn't even take place yet (happened to me before for sure). Producers and engineers often take breaks to refresh the ears (or brain, rather) because our hearing is very variable.
Audible phenomena are measurable even if we can't understand them completely - absolute polarity, for example, has been proven to be audible but we cannot completely explain why and some people don't hear the difference in the same way. But we can definitely show it -
in the time domain. However, I haven't found anyone to have shown this difference on a frequency graph, which is why there still is a debate on its audibility. But in terms of what audio signal is, we know the parameters that influence it, such as frequency response (tonality), distortion (THD(+N), IMD), linearity. Analog signal has only so many properties, it's not magic.
I have long rationalized it as an identity crisis, as mike says - yeah it's relatively unexciting to live in a world where DAC performance is transparent, especially if you grew up in the time of analog audio where a bunch of things from amps/recievers to phono cartridges and needles would make a real difference. But this is no reason to then go on and say, there must be SOMETHING that makes them different. Reminds me of the "I want to believe" alien poster. There are luckily other things in audio that make an incredible audible difference - that's right, buy speakers and headphones, treat your room acoustically, there are so many variables there. The DAC is not going to be a variable as long as it's transparent. Every time someone postulates the DAC difference, I replace every mention of DAC in my head with "high-end cable" and I scan to see whether the arguments change at all, but it's really all the same - I heard it, there must be something, it can't be measured, maybe we're measuring wrong, etc.