I would enjoy it but I would not enjoy all the QQ that would follow... people already want to face tank with ranged DPS class and scream imbalance. People forget the role of support classes, we would have healers mad that they can't do well in 1v1 arenas.
I think if they implemented a 2v2 through 4v4 arena that would be cool. It would eliminate some of the QQ from support classes who try and face tank since they could be teamed up with a class that they could potentially excel with.
All around... I like the arena idea but not for a 1v1. It would be nice to have a dueling area but in no way should it be rewarded in any way. Just somewhere for people to duel on fleet. Honestly I don't even think any arena modes should be awarded if they're ever brought in. Just for entertainment value and practice only.