Again, I don't think the 'story' issue will be quite as big a deal with the 3.0 Expansion Alex. raid and moving on. The problem with the Binding Coil dungeon+it's story is it ties into the 1.0 storyline....which was a casual storyline. So SE basically wraps up the 1.0 storyline (a what 5 year old storyline by now?), which originally was very casual by putting it all in a top-end raid. Sure, the content is 'nerfed' over time....but the people most interested in the story have already waited literally years to see it, and aren't all natural raiders.
It also doesn't help that coil's more or less structured in a way that it only makes logical sense to static it/work with a dedicated team (at least on the most relevant turns)...as it's not even overly feasible for a FC to just assist people through. It's doable, but challenging, both from a scheduling and manpower perspective.
That all said, I honestly think that between the changes made for the upcoming Expansion (Normal and HM versions of top raids) + the storyline NOT directly connecting to casual-oriented content, and instead, being brand new and raid specific, you'll have less 'guys I just want to see the story' posts happening. Binding Coil really sort of is a special snowflake in that it contains the answers/spoilers of what happened with the main 1.0 storyline, and not only was this content far more casual in 1.0...but the way 1.0 players handled grouping/statics etc was actually very different. (people worked together more because 1. the game allowed it but 2. the worlds were so small we had to).
Add to all this: Once level cap increases/new raid and expansion are out, it is likely interest in Binding Coil will plummet. When this happens, it is highly plausible that those folk who really do just want to see the story/clear it once and move on will have a hard time finding folk to run with. Basically, it becomes the Cape Westwind of endgame. Which I think is another reason you hear 'I just want to see it'...people are worried they won't be able to pull together the manpower to do this content once it's out-dated/out-leveled and replaced with shinier content. Also, the news that Binding Coil completion is NOT an entry requirement into the Alex raid likely feeds into this. If binding coil isn't needed as a stepping stone to something else, than there will be little to no reason to do this entire raid post Expansion (the gear will be trash/glamour fodder and the content clears aren't needed for character progression=today's 'endgame' becomes tomorrow's ghost-town)
Lastly, there is a big difference between 'make a story version' and 'nerf it so all the mechanics are gone'. I think, in most cases what people are hoping for is the storymode version to be released at the same time as hardmode, and for the storymode to basically be ala 'nerfed turns 1-9' and the hardmode be the 'original strength' version. Also, they are hoping that by it NOT having gear/desired gear that maybe the lockouts won't affect this content. The lockouts, more than the difficulty are what screw with many people being able to enter/learn the content when it's 'fresh' ....and once new content has come out, it's much harder to find people willing to go back and work on the old stuff with you (nerfed or not).
And again, having the 2 versions preserves the integrity of the 'Hard' version....so instead of SE feeling like the have to nerf the hard content for everyone after a couple months, now they can let the hardmode alone....storymode should be 'easy' enough for the interested/would be the version that got nerfed if people got 'stuck' not enough people were challenging the content. Which I think is actually far more important. Right now, perfectly good, challenging content is 'forced-nerfed' just so it can be DF-able/puggable once it's 'older'....but if instead, both versions were offered from the start, more people would be challenging it (both styles) and there would likely be no need to nerf the hardmode version of the raids when new levels of that raid were released.