The only mount I care about is a Chocobo, but I have nothing against other mounts if that's what some people want. They would need to be specific to FFXIV or FF at the very least. It would be interesting to see some race-specific mounts, ie. only a Lala can ride a Wild Ewe, and only Roegadyn can steer an Aldgoat. Honestly, who wouldn't laugh and take some screenshots at a Black Eft being driven by a Miqo'te that has 3-4 Lala passengers on the back?

The same for vanity pets. I don't personally care for them, but if someone wants a Cactuar, Tonberry, or Moogle following them around town all day, then that's not going to detract from my enjoyment of the game.