Many of the players don't even bother with the chocobo breeding, but i see them doing the races because of the challenge log.

And i know a lot of the players who bothered doing it are not using their race-chocobos anymore, because they farmed way too many MGP already.

So why not let the higher ranked players put their chocobos into a rental service.
Then other players can rent these chocobos out of a list for 100-1000 mgp (depending on the rank), and try them out, and maybe earn better MGP than their own chocobo can. This MGP can be collected later by the owner.
If someone using a chocobo, then noone else can use it at that moment, not even the owner.

They can borrow/rent the chocobos for 30 min, if that time has passed then it will get a 30 min resting time / cooldown (so the owner can get the chocobo out of the rental system if he/she wants to)

Just an example: