I guess the first question is what your definition of "audiophile" is. There is a good article about HD-Audio here:
http://www.audiostream.com/content/...cking-tracks-mark-waldrep#aL1m3zw6qV5UKUfF.97
I'll base my comments on using the definition from the article: "HD-Audio as a recording that has been captured during an original session using equipment capable of matching or exceeding the capabilities of human hearing." I also assume that the goal that you are trying to reach is to at home is to get an exact duplicate of this original sound, or as close to it as you can given your acoustic environment.
There are a lot of pieces that need to come together to make this happen. Your DAC is only one them.
First you have the original recording. Here it is garbage in, garbage out. If a video is shot on VHS tape and then delivered via H265 4K you may get an exact copy of the original. But the original is VHS not 4K so even though it may be mastered to 4K you are still seeing only VHS on your 4K television. So the same is true for audio. So let's assume that the original recording is made on a "state-of-the-art HD digital audio workstation (capable of 96 kHz/24-bit PCM". How is the miking done? Positioning is critical in determining what you hear. Is the audio mastered? That can be detrimental to the sound. If any step in the process of producing the final master is done at a lower resolution, throwing away bits, those bits are thrown away forever even if the delivery method is 96 kHz/24 bit.
Then we get down to the delivery media. Obviously anything that is compressed is thrown out. There are heated discussions about whether not including any sounds above the limited of human hearing (20 Hz to 20 kHz, CD quality) are useful. My hearing doesn't reach to 20 kHz (there are internet tests you can use to determine where your hearing tops out) so in theory just a CD quality recording should be fine for me. A crash symbol can produce sounds up to 45 kHz. But I really hear the difference in high quality sound, in the percussion. I don't know if it's because of the recording or if somehow I'm actually picking up some of those higher frequencies.
I did an informal listening tests with with someone who can hear into the 15-18 kHz range. I played one HD-Audio recording with CD quality, versus the same recording at 96 kHz/24 bit recordings on a home system that can reproduce such sounds. The 96 kHz/24 bit recording was chosen as the best.
There are limited places that you can actually get HD-Audio recordings. For streaming in the U.S. I the only service I know that gets even closed to it is Tidal, which runs 44.1 kHz/16 bit. But on Tidal even if the track placing shows as "High Quality" only by listening can you tell what you are getting. Obviously a Paul Robeson recording from 80 years ago isn't hifi even if so marked. But you really don't know what the quality is of contemporary music really is.
For anything better you have to go to either physical media (SACD, Blu-Ray I think) or download FLAC, Apple Lossless, DSD or other HD-Audio files from some of the HD services - and charge you extortionist rates for them.
Assume now that you have an original source that is HD-Audio. I am assuming from your answer to the question about near-field monitors that you are using a Mac of some kind to play the source material. In the chain we now have the Mac, the cables from the MAC to your speakers, and the speakers themselves. For convenience I assume that you are using powered speakers. [My speakers are a Paradigm MilleniaOne CT 2.1 system (includes a subwoofer)]. How is the mac connected to the speakers? There are discussions about the dropping of the optical output on the new MacPro and how that affects audio quality, and ways to preserve it. I'll skip that discussion here. Given that even an iPhone DAC can produced a relatively decent signal, it is your speakers that really are going to be the most important.
So in all of the components discussed above your DAC is likely the least important, since even the iPhone DAC is relatively decent. This is particularly true if your original sources are compressed or of lower quality. My DAC (Oppo HA-1) handles up to DSD 256 and 384 kHz. But playing a DSD on your mac is a bitch. You have to have specialized software since iTunes won't handle it, and at least one program I have used is really awkward. And if you can't hear the difference, is it worth the expense? If you have a audio dealer that has good demo equipment (such as Goldenear or Definitive speakers, Meridian amps), find a great recording (I can recommend some) and listen to it at home. Then listen to it there. Is the difference in quality significant enough that you want to to reproduce that kind of sound? How much do you want to spend on your system? If you want that kind of sound then first get great speakers. If the dealer has those same speakers, see if you can get him to play it through various receivers or standalone DAC's to see if it is worth the money and the hastle.