[~Wynter~]

Well, that is true that having each character's story being different would make multiplayer harder, but how about this....

Single player - Each character class is able to be customized to suit appearence, etc. Each playable character will have its own role in the Diablo storyline making the game more fun to play on single player since each class will be different.

Multi-player - Each class with have class-specific items (as usual) but also some items that you obtain according to certain choices you make in the game. Class will work together to beat the game using each character's specific profile.

I think that would make the game more interesting and fun to play.