The problem is... nothing really can be done about it. The Warrior of Light is a silent protagonist to further sell the "blank slate" on which every player can project their personality. Since the WoL has to be a blank slate, s/he can't really have a personality, so s/he can't be the central character of the storyline.
DRK 30-50 is a special case because it deals with stress common to every PC. Otherwise, there's no way to tell how X PC would deal with the situation, so we have to be a blank, faceless "white soldier."
While I don't raid, I have watched most of the important Coil cutscenes. What I got from the Coil cutscenes is, again, you are the stoic badass who can endure anything, even striking down the sage-hero (that may very well be your mentor) who saved the world from untold ruin and continuing to shoulder the burden of being "Eorzea's hope." That's the only thing it really said about the Warrior of the Light - the rest was about Alisae, though Nael was touched on in the Second Coil and Alphinaud and Louisoix became more important in the Final Coil.
Louisoix spares you a few words and entrusts you with the task of being "Eorzea's hope," but besides that and as muscle to kill stuff you can be taken out and the story could continue.
The DRK 30-50 quest explores your suffering. Your inner conflict. Your sorrow. Your despair. Your desire. We wear the mask of "Eorzea's hope" and fight the battles no one else can or will, but beneath the mask of "Eorzea's hope" we're struggling and suffering. Nothing else in the game acknowledges this. Every other story in the game can happen without the Warrior of Light because they exist to make others' wishes come true; we are, in essence, the savior everyone wants, not a flawed person with desires of their own. The line in question is the only one that denies "Eorzea's hope" is our true character and deals with the Warrior of Light's selfish wish - to be freed of the endless cycle of conflict and suffering.