It used to be you had to manually dismount before you were able to talk to an npc or zone into an area were mounts were not allowed, like cities. The cast time for mounts, however, is so minor it doesn't really interfere with anything, including gathering, unless you are just super impatient and likely has to do the way the server handles the fact we can summon 1 of over 100 mounts at will, sometimes randomized by the system. That would be a lot of information to store. Most games with instant cast mounts that do not slow you down, only let you have one selected as your mount at a time.

The one mount animation I wish they would bring back, is the small cutscene we got in version 1 when we finally got our chocobo license, which took quite a long time, we had to slow run everywhere for about half that versions life cycle iirc since they were so slow to add mounts. It was short but cute.

Edit: finally found a link to the cutscene https://www.youtube.com/watch?v=9XXVE4hPYYc