Site for those curious:
The odd thing about the ASRock Purity Sound idea...they claim no caps, but there are 9 in the photo...perhaps not in the audio path, but for a "capless" circuit it still rolls of .5dB @ 20Hz. How do you even do that without a cap in the circuit???? Pretty much has to be here somewhere.
And, that wonderful diff amp? Those chips were designed in the late 1970s, it's a dual internally comped NE5534. Big deal. Pretty garden-variety today.
Not to say it's not an improvement over something, but a true cap-less, direct-coupled thingy would have response down to DC, or at least some low limit of the offset comp servo, and there's no reason not to make that pole somewhere sub-audible.
One more thing, capacitors are not always distortion generators. It's just a question of proper application. There are dielectrics that are just fine for audio, completely distortion-less, and there are others than are not good, but can also be distortion-less if used in a properly designed circuit. Most capacitor-related distortion occurs when the wrong type of cap is operated in a circuit where it becomes an element in a filter, or it is operated beyond rated voltages or voltage polarities. Bad engineering sort of gave caps a bad name.