The character restrictions are in regards to the class decks. In order to play in the Adventure Card Guild, each player must have their own class deck. You can play any character out of that class deck, or any character you have unlocked as explained above.
The primary reasoning is that since the Card Guild is organized play, you can take your ACG character and class deck anywhere and play. That would be far more difficult to do if you are taking cards out of the base box for characters and for upgrades to your deck. Using only the class decks means that base boxes remain intact.
It also is a regulation issue. If each class only gets to use cards from their own deck box, then everyone playing across the Card Guild is operating on precisely the same level. It is the same explanation for the regulation in PFS play.