functional
You can't even demat/remat the TARDIS anywhere you want if you build it instead
Why not have it spawn a interior out of bricks
Well, you realize the TARDIS is dimensional transcendental. So, as long as the exterior moves, you really only need to have an interior that is built somewhere. And the main feature of a functional TARDIS is, you know, time travel.
You could have some sort of script such that when you mount the TARDIS it teleports you to the interior. Although, how would you control the TARDIS?
The way I would do it is build a bunch of scenes (Probably a spaceship, a model of Pompeii, etc). Then I would put a TARDIS in each of these locations and have a completely separate interior that links them all.
I don't think there is a way, or even a reason, to make what would be called a functional TARDIS. How would you be able to control the remat/demat? I assume you would be in the interior. At that point, what even is the purpose of trying to animate a re/demat? (Also, I'm fairly certain there is no way to make a model fade in, as I don't think you can change the texture during an animation)