I mentioned this earlier, but usually folks that are wrapped up in lore and story don't actually like to raid (if you truly like getting into lore and story, then you're one of the rare ones.. I know a few others but they're few and far between). It's not their environment, and not something they actually find enjoyable. So the story being the driving factor behind raiding doesn't work with most folks I've encountered. It's a different group of people and a completely different play style. Doesn't make it wrong or anything.
They aren't asking for the difficulty of actual Coil to be reduced, they're looking for a story mode. They don't want the gear, or achievements, just want to see their character in the story. Keep in mind, what is faceroll easy for you or I (and I'm not calling Coil that, my FC is still not past Turn 4), is extremely difficult for some others. Some people can try as much as they want and still won't be capable of downing a boss. While I learn my class almost instantly as I level, and then refine it through research, some people don't have the time to do that, or the ability to learn as quickly from what they look up. There was a thread about a Warrior on a Korean server in WoW posted here a while back that covered that exact thing. He was just a slow learner.
No, not everyone should have the best gear in the game. That's a reward for the most challenging fights. There are achievements for those as well that show you've downed the hardest content. I do not see any harm, however, in making a dungeon to see the story. Unless you're arguing we don't get enough exclusives as it is when completing top end raids by literally being the strongest characters in the game (best gear, and highly skilled).
I don't really care to be a part of some elitist group who thinks they're better than everyone, and should have everything end game exclusive to them. I want a reward for completing the most difficult content, and I realize most raiders want something to set them apart from others.. that's where the gear and achievements come in.
Edited to add: Also, completing the main story typically doesn't signal completion for the lore crowd. Usually they're leveling other characters to see stories from different points, or actually exploring the world to find neat little easter eggs and areas. FFXIV doesn't provide much of that.. but I have seen the lore folks stick with games (without raiding at all) for much longer than the raid crowd. I have a hard time believing seeing the rest of the main story would cause anyone to actually quit unless they were already bored of the game and that was truly the only goal they had left.