As it is right now, having a chocobo level 20 is a challenge, yes, especially because all that gardening stuff and spiritbond with your dear chocobo and etc.... But... It is not so rewarding at all...
Their starts don't suffer any alteration past the level 10, aside of the stats you buy in their three roles, so, yes, you can achieve 45% criticals, around 25-30% hp or so, more attack, speed attack, bla bla, but.... They don't really have a base stats increase, neither anything special at all regarding mechanics or vanity... Yes, you can... Uhm, rather change all of the three special bardings all time or... Use the three pieces of the three special bardings?... UH....
Anyway, here'd be the things that I don't really expect but I'd like to see in level 20 chocobos:
-> Especial colors available to choose when your chocobo is level 20, maybe an option in the stable giving you option to freely change the color whenever you want or even tell you how many fruits you need for achieving each color, also give you possibility to perhaps attain some rare ones such as golden, silver, pure white, pure black?
-> Make them bigger, or make it so they have some kind of glow, or... Symbols or... Dunno, make them a bit special.... (FFXII trickster fan here!)
-> Add a gambit system or give some utility to /cac macro, so we can use the companion skills or order them directly what to do,give us special commands to show the chocobo where to stay, etc... (Similar to pets in that sense)
-> Make it so the chocobo acquires stats from the gear we have equipped, thus, being a bit equal to the ilevel upgrades... As the progress continue we get better gear all time but chocobos still with their low fresh 50 stats... It'd be cool you could for example change to your i110 healer and summon a level 20 chocobo going to have a buff of being summoned with i110 healer, then you change to your DPS and enjoy having a bit buffed healer. (Giving some utility to the fact of having multiple and good geared up classes)
-> More speed... A level 20 chocobo would be worth enough trying if they'd allow us to move faster through the field...This would be A-W-E-S-O-M-E. (And seriously, it feels just odd a level 1 chocobo can run during 30 min non stop at the same speed than a level 20 one, more having in mind they exist basically for transport, a good chocobo should be faster than an average one)
Where's my trickster? T_T
--- My opinion alone doesn't counts. More good ideas of other people! ---
My own addition to that comment, we could have some turbo bard in the chocobo that.... Is increased with the higher the level is... And you have a bit more of turbo speed when it caps at 20...