As roupas refletem como o Doctor está mudando ao longo de sua corrida. Por exemplo, após o episódio de Natal da 8ª temporada, este artigo afirma que o Doctor está acendendo um pouco:
Steven Moffat has revealed that the Peter Capaldi's Doctor will return to season nine much different than he was in season eight.
“We’re not bringing him back exactly the same as we left him, at all. I think that was already evident at Christmas,” he explained. “He’s left some of the burden of being the superhero of the universe behind.”
Então, considerando que ele não vai se mostrar como um herói, ele pode ter sentido que não precisava se preocupar muito com a aparência boa ou não.
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A roupa de Matt Smith mudou .
Wikipédia diz:
The Doctor's initial outfit, chosen within the narrative of "The Eleventh Hour" from an array of clothes found in a hospital, is a brown tweed jacket with elbow patches, bow tie, suspenders, black trousers and black, ankle-high boots. He has a fondness for bow ties and fezzes, proclaiming them as "cool."
The details of the outfit vary, switching from a braces and bow tie combination in red to the same in blue. In later stories, a green military coat makes its way into the Doctor's ensemble, occasionally replacing the Harris jacket.
On other occasions he does not wear a coat and wears a bow-tie and dress shirt. After the Doctor loses his original tweed jacket in the episode "Flesh and Stone" he replaces it with a plain brown jacket which he wears until the Christmas special "A Christmas Carol", which aired the Christmas after the eleventh Doctor's first series. In this episode the Doctor wears his most famous "Prince of Wales check" tweed jacket which he wears, with some switching to a green military coat, until parting ways with Amy and Rory in "The Angels Take Manhattan".
Quanto ao casaco vermelho, a Wikipedia diz:
In "Face the Raven", the Twelfth Doctor sports a red velvet variant of his Crombie coat. After briefly ditching it in "Hell Bent", Clara comments that it made him look more 'doctory'. At the end of the episode, he dons the red coat in honour of her, and is given a new sonic screwdriver by the TARDIS.
Então, dependendo de como ele se lembra de Clara na 10ª temporada, ele pode mantê-lo como um lembrete (embora ele não tenha feito isso com os outros Companheiros, tanto quanto eu sei - e você pensaria que, porque ele estava tão apegado para Rose no começo ele teria mantido alguma coisa).
Claro que poderia ser uma espécie de crise de meia idade como este artigo sugere.