The main reason why this isn't a thing, and probably won't ever be is because of how the devs view the game. Your character can't just "jump in" to any dungeon because you are the right level/ilevel. They have to have a reason to go in there due to the MSQ or the quest associated with it. Each repeat run is hand waved under "you aren't really doing it again, you are experiencing it again with the echo." I know that excuse breaks down when you get new gear and what not from there, but that's the reasoning. The same reasoning is used to explain savage and extreme versions of content. You are experiencing it again with the echo, or as the 'story' that the minstrel is telling. Even the new trials like Sophia EX and what not are simulations being provided by Allagan tech.

Dungeons/Raids aren't just places to 'do.'