you are missing a very important detail here, THE MUSIC.
I use my fat cat when gathering stuff here and there because I like the music.
The fat cat is my most used mount, because we don't use mounts that often after levelling other than gathering/hunts/msq.
Shadow wolf with Hullbreaker Isle BGM ( Horizons Calling) is a disappointment, because we were waiting for a ShB music.
When the "good looking/brand new" effect vanishes, we put every mount (no matter how has been obtained) in the RNG, EXCEPT the mounts with a music we like.
I like the Cid theme 'Dreams Aloft', and this alone make the new mount "interesting".