My point of view and upgrade history in the digital source world concludes:
Yes, there are a great many so called commercial mass marketed CDs which I can only surmise were not at all intended to be played on mass marketed CDPs "IN CONJUNCTION with high resolution headphones appropriately driven by high resolution amplifiers"! Been there, so I added a NOS MHDT Labs outboard DAC and it did wonders for the presentation in that rig at the time with K-701s; However, still there was a problem with many recordings which the high resolution headphones was revealing, as they should, because with great recordings the system then, was wonderful...
Yet there was more yet to be extracted from those CDs of average recording value in my collection, as I found out with this CDP in my signature. More smoothness yet with higher resolution, affording better clarity and details, more refined bass tones, attack and impact throughout the spectrums, as well as added soundstaging both width and hight...
Yet there was still more yet to be added in terms of quantity of degrees of those same newfound qualitys, to the systems presentation when I added/interjected, the tube preamp to the signal chain. To say I would highly recommend a tube preamp would be an understatement, as it is essential to the beatific presentation I'm now experiencing. And this too as a side effect, removed for me any last bit of digital glare to my systems presentation with those same CDs as source material.
All predicated upon the potential capabilitys of the same K-701s and their amplifiers potential, revealing these better signals being fed them through the assembled component chain; Rather than previously the high resolution k-701 and its slightly warm & smooth amplifier revealing the garbage previously sent.
Also, I would add I do like the form factor and availability of CDs and the storage options of digital(SB3 user), so LPs was never an interesting option and i'm wholeheartledly rewarded with each listen, for having persevered...
I can in all honesty say, there is relatively NO digital glare to be heard with my system, yet this is not in comparison to LPs though, but I'm not motivated in the least by any chase to fully try to mimic that because the presentation I was in persuit of, has been realized with CDs as my systems source material.
Point being, in answer to the OPs question; Yes its of course related to the source and the signal fed high resolution headphones, albeit too, a great many CDs were made not at all for high resolution systems, that's why the contemporary mass market media put on CDs is mastered and mixed for their mass market audience who isn't using high resolution gear and compression is fine for boom boxes etc...
But as a medium, CD source material certainly can be mixed/mastered without digital glare or other nasties, as is evident on Mapleshade Recordings, for instance...