I believe that this is because it makes it far to easy to gain experience and make money by fighting time after time. I think that there is a great way to do an arena in an online game though, and it would add a lot to gameplay if done in this way.
First the arena would be large enough for at least 20 duels to be happenning at once, and be in a rounded rectangular or oval shape.
Second, there would be at least 3 gates(min) by which to enter the arena. One gate for low ranking players, one for medium, and one for high ranking (more categories with more gates, or have some days set aside for different ranks (monday loest 3 ranks, tuesday middle 3 etc...
A player could only enter through a gate he was ranked for, and only if another player would enter at the same time. The two entering players, would be dueling competitors, and when one of them one, he could leave, or move towards a fight in progress, in any rank area. When that fight was won, he could select a option(new duel), and click on the player that had just won. it would notify that player, and in 15 seconds(or so) you would be dueling with that person. You would gain rank by beating an opponent of higher rank, or at leat 5 or so of the same rank.
Also on some special days, or just at random times, it might be announced that a monster had just been captured, and was going to be released into the arena in a few minutes. You know just have all 20 or so people try to beat a giant, or a group of 5 large ogres or something to spice it up a little.
Plus have no special rewards, but allow people to watch for free from the bleachers, and allow them to throw money if they want to to a winner, and I think that some people would. Plus it would mean that a dueler that was skilled at making the fight look good would get more coins, rather than one that just went into a slashing fit while running at the enemy.
Also some days could be set aside for magic duels, or archery contests and jousting tournaments. This would add a place for tournaments to be held which can be nice to have spice up a RPG game every once in a while.
Tell the truth and you will never fear someone will figure out you lied.
<<I'm sure I'm quoting someone out there, wish I knew who!>>