Honestly, it sounds like it's just there for the sake of being cool. Both the TARDIS stuff and the fact that it is on a ship. And why would the ship need to be massive if it can be any size on the inside? Why not just have a Galaxy-class size ship inside a shuttlecraft?
And why do they need a training facility on a ship? If it's like a training vessel a la USS Valiant, then it's understandable (but would they really use this TARDIS technology on a ship like that?), but it sounds like it's just a ship they've decided to put a school in, and I've gotta wonder what the benefit of having a school that can fly is. Why not just have them going to the academy on Earth and when they need to be on a ship they can go on a dedicated training vessel?