I'm pretty sure if some random mechanical cat on a Moogle doll tried to join my party for no other reason than to supposedly see how a fortune turns out I'd be saying thanks but no thanks.

Hahaha spot on :P

I would also add that the story is weakened by Cait. To have that thing roaming about with your party makes the plot look stupid and the plot is dealing with some serious issues:

Death, Misery, Suffering, prison, Friendships, Suicide...they are all in the game, and having a bouncing stuffed toy in the middle of it just ruins the dramatic side to things.