Why should this be different from other games? You can't see the ending of Mass Effect without beating the game, you can't see the final ffvii scene if you don't beat sephiroth...
The coil fights themselves are part of the story. The cutscenes are what happen after the fight. Why should you see the postfight cutscene of a fight you didn't participate in?
I feel for you if you can't beat it and all, but I don't see why people think this is a unique problem to MMOs or to ffxiv. You have to do content to get the story in pretty much every video game ever.