Wow! Is that scale correct? You're looking at over 2,000 kilometers in diameter?
Yep, think about it this way, the main structure of the tardis is grown by using carbon fiber, then the massive work is done through robotic and matter conversion techniques.. this allows the Time Lords to manufacture a massive ship, which can hold the sum total knowledge of an entire sector of the Galaxy.. remember, as the Tardis lands on a planet, it creates a holodeck like environment, which is a duplicate of that world, thus the time lords are able to view and explore in safety and comfort within the ship itself..and then move forward in time to see how the society progresses.. I think they were banned from going past a certain point..like say normal Gallifreyan time zone..anyhow, yeah the Tardis is a massive ship, and it has to be because the ring like engines which force the time vortex into being have to be massive to control and move with such power it takes to do that..kinda like a hyperspace worm whole.. only the tardis is in it's own dimension..
Honestly though, think of how big the explosion was that lit up the sky on earth in the recent 5th season of doctor who, episode "the Big Bang" and if the ship can generate that massive of an explosion, then think about the size of this ship's design and you can tell that it is a massive machine!
Oh, I understand your rationalizations for the size, but I'm rather stunned by something this big. Sure, the TARDIS is bigger on the inside, but this thing dwarfs the moons of Mars. If this landed in Washington, DC, it's shadow would extend past Boston. That's really ... big.
What do Timelords do with all that space? How many typically staff such a vehicle? I have to admit that I'm not familiar with this holodeck function you mention. Certainly, I don't recall the Doctor ever exploring anything in safety and comfort.
Although, the TARDIS did
tow Earth across the cosmos once. That's not exactly the job of something tiny ...