How about at 1.19 patch, Doh/L get a quest at r25 that grants them to breed the chocobo, It is only available to DoH/L that have pledged allegiance to a Chocobo Breeding Guild. Will pure battle class cry for it? Think before you answer it.
This sounds like it would only make sense to me and im a battle only player who plans on owning his own Chocobo.
luckily i think the current lore would be that your Chocobo was issued to you after being raised in the GC stables leaving a whole lore background for DOL/DOH when it comes to actually raising them.

Perhaps this could be the Herder class already in game (there are wooden banners for this class in.... Thanalan i think?) and they could even sell their super raised on steroids Chocobos to other players!