Wow, I never thought of that!
I think it might also add some flavor. After all, there's got to be an announcer in the Mage Wars Arena right? And the crowd will be more interested if they know a little bit about the mages fighting. Like this:
"In the western corner, a monster of a man with a heart of ash, burning with darkness, a nigh-undefeatable warlock said to be a demon himself, (WARLOCK'S NAME HERE)! And in the eastern corner we have a powerful forcemaster, the might of her mind has crushed all who stand before her in a nightmare of blood! (FORCEMASTER'S NAME HERE)!"
Also, I think something to keep in mind flavorwise is that at the beginning of the game, the mages don't necessarily look like they do on the cards. No armor, no cool-looking creatures or magical items. All they have is their spellbooks and the clothes on their backs. This means that without the announcer, neither of the mages know what type of mage the other is until they start casting spells. But in a game of mage wars, both the players know, and can start strategizing of how they're going to deal with the particular mage they're facing before that mage starts casting any spells.
I think that revealing training is important not just for gameplay, but to prevent a disconnect between gameplay and flavor.