So how come The Great Hunt can't be unsynced?

[Hezzlocks]

I feel that you should be able to play all content unsynced, but that rewards should reflect this.

So if the Great Hunt were to be unsynced... no mount reward.

An alternative would be the way WoW handles mounts, too. If you clear the Mythic raid while it's relevant, 100% drop rate (doesn't necessarily need to be 100% in FF14 of course, just keep drop rates as current). The moment it's no longer relevant, ie, doing old content unsynced, the drop rate plummets to an abyssmal 0.1% drop rate. You want the mount? Put in the work, one way or the other.