While i understand your desire to experience the story within content that you have yet to complete.

as you asked "Is it right I cannot experience the story behind raids as the Coil?" short answer would be yes it is right.

But that is only true if you give up, part of wanting to complete the story of any content. Is that you aswell as your friends work togheter to overcome a challenge and achive something togheter.

And if we look at it from the other perspective of those that want even harder content, is it fair that all content is made easy just so everyone can experience it? Too remove any need to work and improve and challenge oneselves? I dont think that would be fair or reasonable.

There needs to be different types of content in a game for many different players, fun,easy,difficult and so on. And we as players need to focus on what we ourselves choose to value, and acknowledge when some content is out of our reach at that very moment. But that is no reason to give up just because something is difficult, work hard maybe you will clear it maybe you wont. But that is no reason to surrender and wish for easier access.

However with Heavensward the raids will have a storymode and hardmode, so they are going the same route as Blizzard did with world of warcraft.

As for right now and the content in ARR i understand your desire to experience the story, as do i since i have not completed it all myself yet. But i wouldnt want to see it being made easy for the sake of convenience.