A warm DAC?

Fair point. But your determination (or mine) does not become the de-facto metric for everyone. 

I think in this audio arena the most useless term is “always”. I find that almost all absolutist statements can be countered with “it depends”. 
Folks in this hobby mix and match all manners of tube, solid state, Class A, Class D, etc, equipment in an infinite array of combinations and price points. Some are very casual and some approach this pursuit very intently. 
Some believe 100% in the “bits are bits” approach and never waiver from thinking that streamers, DACs, cables, different interconnects, power supplies, reckockers, isolation feet, racks, etc, etc, matter. Others think it all matters. 
In the end what counts is this: do you enjoy the music from your system? Are you ok with the money you have spent to get there? 
  

Audio Note has an interesting design philosophy. They build a component and of course take measurements, record the specs, then they listen to it.
They make adjustments until it is pleasing to the designer's ear. The owner of the company is the first to admit his products, in this case DACs, do not have the best specs when measured by an independent source. But they're doing something right because their DACs sound wonderful, like real music.
And they are coveted by owners who pay high prices for these well designed, well built Dacs containing premium parts. 

It's also interesting to me that when describing a component as full of distortions, that analogue turntables aren't mentioned. The vinyl medium that many prefer to digital is full of distortions and colourations.

I'm auditioning the Mytek Brooklyn DAC+ with PrimaLuna HP integrated. They sound great together! So much so that I'm buying the DAC and an EVO 400i.

I'm not sure I said always. I have heard differences in DACs but not DACs that measure very close. IMO the DAC is the least component to concern yourself with. Get one that measures well so you get what the artist, sound engineers etc.. intended, what's on the recording. Tube amps, EQs, tone controls, Room Correction software, flavor of speaker, room acoustics and treatments, speaker position, there's enough there for me to figure out without getting a lousy measuring DAC like a Border Patrol which is the one I was talking about in the first place.  I mentioned about 5 or 6 DS and R2R DACs that the OP might consider or not. 

analogue turntables aren't mentioned. The vinyl medium that many prefer to digital is full of distortions and colourations.

I never post on the analog section I quit listening to vinyl and tape years ago.