Doctor Who: 20 Things You Didn't Know About The Tenth Doctor
13. His Clothes Are Crumpled On Purpose
Like any major franchise, Doctor Who has loads of extended universe media that builds on (and contradicts) the main canon of the show.
Let's look at the comic-books here, and more specifically, one issue that was brought out for Free Comic Book day in 2015.
In this story, the Tenth Doctor and comics-exclusive companion Gabby are cleaning themselves up after a messy adventure.
The Doctor shows Gabby the TARDIS' laundry system, which cleans clothes in the most wibbly-wobbly way possible.
In an exchange with her, she mentions that there's a glitch in the system that means the clothes always come out crumpled.
So there you go, that's why the Tenth Doctor always looks like he's never seen an iron in his life!