I think they initially intended to have Bowser Jr. be one of the characters working for Bowser in story mode. But the problem was, they didn't want to make him a playable character as he wouldn't make sense due to being Bowser's son. Bowser doesn't care about Koopa Kid, so he could do anything with him, but Bowser Jr. wouldn't be given such treatment.
So based on this, they probably scrapped the idea and used his leftover animations for Bowser Jr. mini-games. It is expected that they made all the model animations before actually programming him as a character, and just found that he wouldn't work out in the game (especially since they needed to make a mid-stage Boss for Bowser's board).