No, Sherlock always externalizes his thinking, that's what he needs Watson for. When Watson wasn't there he would talk out loud to a skull. He always explains his thinking as the case is going along, unlike a ti detective like Poirot (INFJ), who is totally mysterious about what he's thinking until the "big reveal".
Isn't he just saying what he's thinking when it's necessary for the plot? Your argument sounds solid, but there are plenty ones for INTP as well.
It's been a while since I've read the books, but in the BBC show, he seems more like a J type to me; probably INTJ. Cognitive functions aside, he seems to come to conclusions much more readily than a perceiver would. Even with his extensive knowledge, how does he narrow down all possibilities to a single, definitive answer so precisely? He doesn't seem to spend much time actually theorizing as he does deducing. Not only is he quick to make decisions, but he doesn't seem to have ANY doubt about his conclusions. Sherlock comes up with the most bizarre correlations too. It always leaves me wondering how someone who is so meticulous never has any reservations. I would imagine that a perceiver would at least consider a remote possibility that some other explanation might exist.
How can so many people think that BBC Sherlock is INTJ?
There can be no Sherlock (or at least I can't imagine Sherlock) who isn't Ti user. And BBC Sherlock is definately Ti user, the first thing he does is noticing details and patterns, making connections between them, understanding how things work.
It's true that Sherlock is making here some detailed and advanced plans, but it's all a game for him, part of the puzzles or chess game. I think that comparing him with Mycroft shows the best the difference .
So I think:
Sherlock is INTP 5w4,
Watson ISFJ 2w?,
Mycroft INTJ 6w5
“The world is full of obvious things which nobody by any chance ever observes." A.C. Doyle