Mounts are a great way to get around . But surprisingly, there is relatively very little advantage to speed: instead the advantage is carrying capacity. Mounts can carry more than humanoids can (PHB 157).
The only speed advantage come that they can double their speed for just 1 hour (galloping) – which is a short time when covering a long distance.
Fun factor – a character could possibly ride a land mount, flying, swimming, climbing, gliding or maybe even burrowing mount.
Animal handling – Flying mounts need to rest 1 hour for every 3 hours flying (DMG 119) for a total of 9 flying hours per day (Fly 3, Rest 1, Fly 3, Rest 1, Fly 3, Rest 8)