I like the idea of it and it kind of just throws money at you. I was just curious if there is any reward (like a TM or held item or Mega Stone or something) besides having access to a bunch of trainers that you can fight a lot?
Getting to the second-highest rank (Marquis/Marchioness) and highest rank (Duke/Duchess) unlocks rematch battles with the Gym Leaders and the Elite Four. However, without Writs, the Elite Four actually end up using lower-level Pokemon (around 40). However, after using several Writs, the Champion can end up using up to level 80 Pokemon in a rematch battle.
Higher-rank trainers also have a chance of giving treasure items such as Big Pearls.