Mount

[Enkidoh]

And the Company Seals are gained automatically by completing FATEs once you've joined a Grand Company so you don't really have to do much more than a few FATEs to get the issuance (note, it's not actually 'insurance' but 'issuance' - it's basically a driver's license for riding chocobos.)

Once you have this issuance and completed the above quest, besides gaining your default Grand Company chocobo, it also unlocks all other mounts you already gained as well, like the Collector's Edition bonus mounts (Courel and Fat Chocobo), and the special Legacy chocobo (if you're a 1.0 player with 'Legacy Campaign' eligibility). You just have to open the 'Actions and Traits' menu and click on 'Mounts' and then click and drag the mount's icon to your hotbar. You'll then be able to ride it whenever you wish (other than when you're in battle, in a dungeon/instance, or in one of the three cities).

[Suki-]

'issuance'

Lmao. I always thought it said insurance XD there's another bubble burst along with camp bluefrog ^.^

[Niwashi]

(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.