As Turpster would say, it definitely gives you a nice overview of how all the classes work and what their strengths and issues are. And of course it'd be handy to run instances with -- you can roll into endgame instances playing whatever role you want or your guild needs to have.
But as has been said before, I'm always a better player personally when I'm focusing on one character rather than splitting myself up. Even if you do have the time and interest to play each character regularly, it can't be easy to keep all of those various spells and abilities and talents straight in your head. Not to mention that all of that time spent leveling is time taken away from working on endgame reputations (there are certainly plenty of those to grind) or doing something else like endgame raiding or PvP. If you just want to join "the club" for bragging rights, that's one thing (and more power to you). But is there really an advantage in the game to having one level 80 of every class?