So it turns out Gallade has a normal running animation rather than using telekinesis to make himself float, unlike the running animations of his family members.
Looking at all these running animations, I thought just crossed my mind.
While it's possible the Pokemon-following mechanic was planned for Sun and Moon but was scratched, what if it is something they built in the game's programming but they plan on releasing it in a future Pokemon game? Think back to when we first learned about the Mega Latios and Mega Latias. They first appeared in the coding for X/Y, but they weren't officially released until OR/AS came out. Perhaps it could be a similar thing there? Maybe they will bring back this walking feature either in the Diamond/Pearl remakes or Pokemon Stars (depending on which one we get this generation), but they only added it in Sun and Moon's coding just to one feature out of the way in terms of development.
I don't remember if this programming-into-initial-game-but-will-be-saved-for-later-game has been discussed here already, but in case it hasn't, I just wanted to throw it out there as food for thought.