I am not going to attempt to convince anyone with measurements or empirical data, but I've done a lot of headphone listening with mid to high end headphones, amps, dacs etc. From my own subjective opinion...
Schiit has a great reputation in headphone hi-fi circles and I'm sure they make wonderful products. But I agree with those who speak of a wall at about the $500 price point.
I have compared my own system (w/ Emotiva Stealth DAC) head-to-head to a couple of headphone amp/dacs (combos and separates) that cost several times its price by brands like Naim and Ayre. I don't know models off the top of my head but I'm not even considering the expensive cables balanced cables in these setups. My system uses nothing but cheap interconnects and stock headphone cables.
I can say definitively, as a total, unrepentant audio addict that multi-thousand dollar headphone components bear no interest from me. Sure, they're great sounding, but so are my...
Emotiva Stealth DAC + Antique Sound Labs tube amp + Audeze LCD2 ... total investment <$3K
The Naim & Ayre setups were running between $5 & $10K (not counting the headphones)
Critical listening resulted in no obvious differences in quality. Yes, I heard "differences" but nothing I would call "better". For thousands of dollars extra... I need to be blown away!
By blown away I need to compare and go... "HOLY MOTHER OF GOD!" I have seen this very reaction in people blown away by audio when I've introduced them to better setups than their shitty earbuds plugged into a cell phone.
<$75 earbuds plugged into a cell phone... total investment <$500.
That's an investment differential of only $2.5K for "HOLY MOTHER OF GOD!".
But from my $3K system to a <$10K for a difference I can't really put my finger on whether or not it's actually better or my imagination? It's just not worth it.
But that's just me... your milage may vary.