So, let me make one final and clearer post on my point of view because I feel I wasn’t clear when arguing with Aguni, mainly because I’m bad with expression and English is not my native language.
So first: Teron Gorenfiend has red eyes.
Yes he does. He is also a First Generation death knight, meaning he is a fallen warlock possessing a fallen Stormwind knight. It can be said his red death knight eyes are nothing more than his orcish warlock eyes (see Gul’dan for proof of orc red warlock eyes), that indicates his essence taking over the fallen knight body. The reanimated bodies were also just that. mere reanimated human shells, nothing special. They did however had tremendous magic powers.
But why do our death knights doesn’t keep our racial eyes, since in theory, reanimation is the act of putting a soul back in a body, much like possession? Well, this can be explained by the difference in the method applied. For the first generation death knights, Gul’dan simply put the souls of fallen powerful orc warlocks into a reanimated knight body. For our generation of death knights, their bodies, and soul, are infused with the Lich King’s power, and not merely reanimated like the forsaken or first generation death knights. The lich king’s power changes the very core of their body and souls, granting them his powers, his being, his everything. He wanted to make them his image, hence why they have unholy strength and powers. Wich also explains why their eyes take on the color of the Lich King eyes.
So to sum it up:
First generation Death Knights: fallen orc warlocks spirits possessing fallen human knights. They didn’t have more strength or martial prowess, instead keeping their great warlock magical powers.
Third generation Death Knights: fallen heroes of both the Alliance and Horde, reanimated AND infused with the Lich King’s power, granting their bodies superior strength, among other of his powers. Made in his image, having some of his physical traits. This is all is shown in the first thing he talks to a new death knight:
" All that I am: anger, cruelty, vengeance - I bestow upon you, my chosen knight. I have granted you immortality so that you may herald in a new, dark age for the Scourge"
So, playable Death Knights are supposed to be lesser versions of him.
And why the Lich King have these ghostly phantom eyes? Don’t know, ask Blizzard. It is what it is. Bolvar mostly kept his “revived by flames” appearance, even while using the helm of domination, but as seen in the last trailer, the moment he goes full on Lich King, his eyes, scars, weapon, everything glows ghostly blue. And no, he doesn’t need to be full on lich king to be mind controlling the scourge, because as we have seen with Arthas, it’s a menial task. He mind controlled the scourge while being greatly active, doing various other activities at the same time. If it was that hard for him, he wouldn’t be able to do half of what he does. He only lost control briefly due to being almost stricken down. So no, Bolvar probably didn’t have to tap on his full Lich King powers just to keep the scourge in line. He did however need it for powered up Sylvannas.
As to other Death Knights shown that has no blue eyes.
Thassarian: has no blue glow on his eyes on his ingame model, however on the very cover of the Death Knight manga his eyes are glowing blue. That inconsistency alone is enough to invalidate his example, as it can be many things. His eyes may only glow when using his powers, blizzard also may have effed up on his model and it’s not worth redoing it, it can be many things.
Lady Alistra: has red eyes. However, I’m yet to find any source that states she is a Death Knight. Most sources cite her as undead Blood Elf with affiliation to the death knights, as unholy trainer. As we know, death knights trainers aren’t always death knights, since Amal’thazad, the frost death knight trainer, is, well, an Arc Lich. A quick small search will only mention Lady Alistra is an undead blood elf afiiliated with the Death Knights of Ebon blades, and is their trainer. You know what other undead Blood Elf has red eyes? Sylvannas.
Now I believe those 2 are the major examples people were using on this forum. They can also be very easily invalidated as examples, as per motives above.
Now everything I said, can be easily researched in the Death Knights lore. And all gaps were logically filled, because, as we know, blizzard haven’t been exactly consistent on things.
And that ladies and gentleman, is why I believe the ghostly blue eyes are indeed part of the Death Knight identity, and having more customization for it would ruin it for people that like the lore behind Death Knights. Sometimes, less is more.