(Edited)
Oh my...
Point-value based teams having it out on your screen!
Randomly generated teamates, some built on the Theme basis.
And, if you're honestly considering throwing tourneys in as a plot device, here's a few thoughts.
An underground arena, not a requirement for completing the other arenas because it is not officially recognized.
Random chance of your Nemesis showing up in the arena, slightly above the target difficulty level. Probably not going to happen unless he's within 50% of the PV you're set to face.*
(Edit) Alternatively, simply weave the arena battle into a manhunt for your character, as in GH1 when AOL would send an individual after you. In this case, have it be more likely just a higher-than-appropriate random opponent, and have the arena owner comment on how the match-up was highly irregular. Essentially, a plot element in an otherwise ongoing manhunt for you might be inserted in an arena battle as a clue to the next phase.
Chance of developing a nemesis by winning against random theme opponents in arenas. Preferably only one nemesis per game, but it would be a heck of a way to get one.
Randomly picked element (based on a Leadership check modified by number of lancemates?) of themed opponent who loses in the arena showing up and asking you for a job. Best not to happen often, maybe set as once-only. "With my mecha gone and me out of the championship, I figure I may as well go with a winner, especially if you've got a mecha for me." If the player says yes, it might be best to eliminate the theme from the character's description thereafter; equipping said character with an Esher emphasizing missiles would make Fire dialogue pretty dumb.
* However, if you'll consider random lancemates for a gameshow arena, it would be immensely comical to have the nemesis spawn as either a "friendly," with a Lawful check to determine whether or not s/he'll turn on you, or as the only enemy on the map because s/he's sure s/he can take it. Pretty consistent with some of the nemesis scripting I've seen.

"I knew I'd find you here! Ever since you left me for dead in that duel, I've been hunting you, and finally I've found my chance! You die today! By FIRE!!"
If this happens, it should launch conversations, I think. On another note, if the player decides to attack the "friendly" nemesis on that same basis, there should probably be repurcussions.