Just watching Fugitive of the Judoon and I can’t make sense of that particular aspect. I’m sure there’s a discussion around it somewhere but I can’t find it!
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The TARDIS likes being a police box.
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Personally I don’t think there’s any big in-universe explanation, or maybe tbh I just don’t really care. I think it was just done to be more impactful for us, the audience.
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Realistically, if a marble pillar gets unearthed and the Doctor says “That’s a TARDIS!”, it really isn’t going to hit nearly as much as a police box.
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The simple answer: it’s instantly recognisable even for casual viewers. If it looked like a generic gray capsule or something else entirely, a lot of people wouldn’t know what it is, and they’d have to explain it with dialogue, therefore making the scene much less impactful.
The complicated answer: who the hell knows?
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So the Fugitive Doctor is on the run, about to Chameleon arch herself human to hide. Clearly decided on Earth, England. Chameleon circuit decides that a police box is some old Earth English artifact that no one would think about so it becomes that on landing. She chameleon arches herself, and her “companion” for lack of a better word buries the TARDIS underground, where it stays. I don’t think there’s anything more to this, and I don’t know why it’s such a sticking point for people. Sure, it’s speculation and not explicitly stated by the episode, but it’s perfectly consistent with what we saw.
Out of universe, well yeah, to be recognizable to the audience.
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I believe there’s two explanations, one on BF and one in the Comics! On what those are… I forget 
I think BF’s one was the TARDIS just looking into the future and sticking with it?
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The TARDIS looking into the future makes sense – she is a time machine so what’s to say that she experiences time in a linear order? Maybe the Fugitive Doctor’s TARDIS can ‘remember’ being a police box in her own future as if it’s her past.
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Or it can pick up on other copies of itself, and has seen all the many times that the TARDIS has landed on the earth while it was buried there, mostly in the shape of a police box, and changed shape to match.
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Just skimming through Origins, and I can’t seem to find anything about the TARDIS being stuck as a police box…
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Honestly, with how many plausible explanations we have come up with already, I really can’t see why so many people had a problem with this…
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I didn’t like it and still kinda don’t Tbh, I still headcanon her as 2.5 so works that way for me.
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Yeah, that’s another way to explain it!
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From the audios, Fugitive Doctor says it becomes a police box at some point and gets stuck, so it is faulty already.
The TARDIS is then put into a repair shop and the Fugitive Doctor has her memories wiped and becomes the First Doctor.
Then the First Doctor steals a TARDIS and happens to steal the same faulty one. Either because the TARDIS “chose him” (The Doctor’s Wife), or because Clara told him to (The Name of the Doctor).
This same TARDIS is still faulty so when it lands in Earth 1963 it gets stuck again, this time stays stuck.
And also it just helps the audience understand the gravity of that scene.
Anyone complaining that it doesn’t make sense or is a plot hole clearly can’t remember that in Serial 1, Episode 1, it’s stated that Susan named the ship the TARDIS, and we don’t still believe that, so the canon can change to fit the show 
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Aaah, the golden days—when the Doctor and Susan were potentially humans from the future or aliens from another planet; when Susan named the TARDIS herself; when the Doctor had just one heart and couldn’t regenerate; and when the Doctor smoked pipe like a gentleman!
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Maybe the TARDIS liked the name Susan gave it, and its translation circuits translate any reference to it into that name?
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It also isn’t necessarily stuck as a police box either. It just is one.
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And Fugitive Doctor is pre-Hartnell, to quote 6, “whether you like it or not.”
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Oh I meant Fugitive’s specifically. The Doctor we all know, it is stuck except for that brief time the Doctor tinkered with the circuit.
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