This is what I was thinking going along with the OP's idea. Give mounts a little bonus in certain areas. Something nice to have, but isn't necessary.
Maybe certain ones have a lesser/no chance to be Heavy'd in certain areas (like, the Elbst in Sahagan-controlled areas, or Drake in Amalj'aa territory..sorry, have to deal with it in the Sylphlands >

), lesser chance to aggro mobs in places (maybe ADS and Twintania in Azys Lla would do this, or Middy and the Wyvern to dragon-type enemies...or any mount to similar mobs)...stuff like that. Nothing game-breaking (though, maybe make the GC Horses only have a chance to Heavy when struck in Frontlines rather than 100% chance.but ONLY when you are on the correct GC. You earned the horse after all...)