I think you miss what OP was saying. We have discussions on what we want, and mostly don't want in a relic quest, what OP was saying is, could we have a story again that is tied to the relic itself?
2.0 and 3.0 relic felt like I'm doing these quests -for- a relic. I especially liked 3.0 with how you interacted with the anima, got to chose if it's male or female voice, I wish they did more with it but it still made the whole process feel all the more personal.
FF14's strongest point is story and lately that's been lacking imo.
4.0 relic to me felt like, I'm helping Krile solving the isle of Val mystery cause I'm the WoL and I'm getting shiny weapon on the way as a bonus. The two stories don't feel tied together, maybe they will connect at the end, who knows. The relic just doesn't feel like a relic.