I see this other times, such as when Fates end, but the Beastman Daily Quest, Hatchling Humiliation, is the worst for this issue.
When you finish defeating the Hatchling, you douse him with water. After dousing, he does a dialog which you clear. After that, sometimes I can mount my chocobo right away and sometimes it takes up to 15 seconds before I can do this. There is no pattern but there will usually be at least 1 of the 3 you defeat that will have this delay.