Well I think we arrive now to the definitive question: does DoP sounds equally to native DSD? I personally think NOT. I have an IFI Micro DSD that plays native DSD and you can hear the difference when you play it on DoP, I have read a review in Head-Fi and this is what it says:
"I mentioned earlier that iFi doesn't follow the hi-fi norm. What does that mean? iFi believes in minimal DSP, and believes that one should be listening to as close to the source audio as possible. DSP's such as upsampling, volume control, format conversion, etc. create unavoidable mathematical losses. The more conversions, the greater the losses. The more changes to the source signal, the more likely the changes become audible. This may especially be the case with DSD. DSP such as filtering, sample rate conversion and volume control require conversion of the 1-bit bitstream to a multibit intermediary, and remodulation back to 1 bit.
Therefore, the iDSD Micro uses a chipset that converts DSD to analog natively with no extra digital conversion or DSP. The 1 bit DSD signal is sent to an analog FIR filter for conversion. That's it! Also, the iDSD micro has a 'BitPerfect' filter option for PCM. This eliminates the oversampling reconstruction filter used in PCM conversion."
I guess Chord is always better in PCM than in DSD, don't know why they have an ASIO driver if you can't hear native DSD anyway, what is the improvement from changing from WASAPI to ASIO if you still can't hear DSD native files? Other DAC brands as Fiio or iBasso have moved to play pure DSD instead of DoP, can't understand why Chord not ...
First, The Head-Fi quote has nothing to with DSD over DoP. It applies to various DSP and other operations on the signal, but not to DSD over DoP. DSd over DoP is a bit perfect operation. The operations in the quote are generally not.
The"format conversions" in the quote is questionable. Lossless conversions do not affect the final sound unless there is a problem with the conversion. Lossless to lossy converstions do.
If native DSD sounds different than DSD over DoP, then it is a problem with the implementation. Converting a DSD file to DSD over DoP and back to native DSD is bit perfect if done correctly.
Here is a oversimplfied example
The DSD Signal is 1001. DSD over Dop simple packs 1001 into a PCM wrapper, but the 1001 is still there. The input stage of DAC simply extracts the signal from the DSD over DoP and it comes out as 1001 and passes it down the line, just like it would do with a native DSD format. The operation is bit perfect. If the player and DAC do their jobs correctly, then you should hear no difference in playing native DSD and DSD over DoP. Again, the only use of the PCM format is to move the 0's and 1's of the original DSD to the DAC. The DAC extracts the 0's and 1's and then processes the DSD signal.
If you hear a difference in native DSD and DSD over DoP it is an implementation issue, specific to your equipment.
I am not sure why Chord implemented an ASIO driver. Maybe they just wanted control over the transmission and figured ASIO was a better option going forward. But is has nothing to do with sound quality.