I don't think the initial experience needs changing and I don't think the OP is suggesting that either. First time through I read all the text, watched all the cut scenes and generally enjoyed the story. That was my first character back about a month after the game opened. Now I have two alts which were also required to push through the same story quests and a fourth I just don't have the hear to do it for. I think the way things are for your first run are great, perfectly fine. The issue arises for those of us who do not want our huge manly tank running about in healer robes and so we make a new character.

More or less, after three runs through, I feel that it should be the same if I jump to a new character as it is if I have a 2nd class on an existing one. Especially considering how long the patches have started to make that journey and the impending release of new races which encourage the making of alts.