Quote Originally Posted by Enkidoh View Post
(note, it's not actually 'insurance' but 'issuance' - it's basically a driver's license for riding chocobos.)
If you're going to equate it to driving, it's more equivalent to the title to your car rather than your driver's licence. The Grand Company is giving you (i.e. issuing you) a Chocobo, and the issuance is the paperwork telling the chocobo keeper that this chocobo now belongs to you.

Completing this quest does unlock the use of other mounts if you have them, but there's no in-game lore explanation of how your character comes to have any of the special Collector's Edition mounts, or how riding them would have anything to do with your chocobo.