Frankly, I think it would be nice to get away from the Doctor having a real trademark look. What if the 12th Doctor just kinda wore stuff that didn't really draw attention to itself.
Although, I do think that the 12th Doctor should have a strong aversion to ties. "Ties are pointless." (In fact, I'm having this vision in my head of the Doctor ripping off the bow tie in disgust. Then, he comes to realize that the rest of his wardrobe is superfluous as well. By the time he's done, he's stripped down completely naked and Clara is struggling to think of a polite way to remind him that "People like clothes on other people... Just, generally that's kind of a thing...")
Smith, well, we remember the fez and the stetson mainly because River shot both of them, but he didn't wear them on a regular basis.
He also donned a top hat a few times: "The Big Bang," "Let's Kill Hitler," "The Snowmen." It may not have been a regular thing but it looked really good on him.