I don’t think a trench coat would suit all of the Doctors, and you don’t want them all to look the same anyway. I remember when the wardrobe dept were talking about Eccleston’s look and they were talking about things like his silhouette, everything. So whilst I don’t think the 9th’s look is a great Doctor look, I think it’s perfect for the 9th Doctor. Sticking a trench coat on someone like McCoy would have been terrible, in fact I’m not sure even Smith could have pulled it off the way Tennant did, but then Tennant wouldn’t have pulled off the absentminded professor look nearly as well as Smith.
And I’m not sure if anyone else could have worn most of Pertwee’s outfits