Personally I have zero problems A/B-ing DSD, PCM and lossy formats on my reference system (headphones). I also know (award winning) people in the audio industry who can walk into a listening room and tell you where the dominate resonances are or tell you if a reconstruction filter is linear or minimum phase.
The idea you can take a group of non-professionals and run tests with no requirements on equipment quality and then draw conclusions about what any human can hear is absurd.
Those tests (Hydrogenaudio was one of the main proponents back when lossy codecs were more important) are a decent way to tell if something is audible for the average listener with average equipment. It cracks me up when people start telling me what I can or cannot hear based on those tests without knowing anything about me or what kind of equipment I own. This happened just the other day on an audio forum.
Another dimension to this is that DAC quality has been increasing steadily while the prices of high fidelity DACs have been dropping. The DAC chips on the market today are really the best ever made (ESS and AKM notably). More people than ever have access to (near-)reference quality DACs. When lossy compression tests were popular few people had access to reference quality DACs. I remember people talking about using their computer sound cards as sources for those tests.
I think a lot of people react negatively to this topic because it's considered elitist (expensive toys). The good news is just about anyone can afford a near-reference quality, inexpensive headphone setup these days. You have to do your homework and read reviews but they definitely exist. I recently picked up a DAP and IEMs for ~$300 total (for running) and it's 90% of the quality of my reference rig. I listen to it instead of my reference rig sometimes. It's that good, despite the price.
(Even on that, I can easily ABX FLAC and 192kps AAC, which has been universally declared "transparent" more than once.)
If you think your smartphone's audio jack sounds good, you really need to listen to a device with a proper amount of output power (you need more than you think for headphones) and a high resolution DAC. You need both to be good, though they can be part of the same device. When you have them, music really becomes holographic and, for lack of a better word, alive.