Keirsey explains that people of any temperament can do tasks more naturally done by someone else, with effective IQ dropping depending on how far away from one’s core m/o the task is. On page 312 of his “Personology” book, Keirsey estimates the drop off for an INTP with an IQ of 150:
INTP tasks- 150
ENTP tasks- 140 to 145
INTJ tasks- 130 to 135
ENTJ tasks- 125 to 130
House is INTP, but as a tremendous genius, he can still show great competence and flair in doing more stereotypically INTJ stuff, like the elaborate trolls of Wilson and Cuddy that require sequential chess-type planning of the moves.
To briefly justify his typing:
N- Don’t think anyone is claiming he is an S; we all saw the N.
T- He does indulge his F impulses, but the luxury of doing so in his way is afforded by his super T that is exercised the rest of the day.
I- Yes, he likes working with others to get the ball rolling in a “pseudo-Te” manner. But if you notice, his flashes of brilliance that end up solving the puzzle come from within. He is talking to Wilson about something seemingly irrelevant, when a lightning burst of Ne will connect the patient to the conversation in an unexpected way. Also, he chooses to spend his free time alone at home, outside of phoning the occasional call girl. Not really someone who is energized by E experiences.
P- He is a classic “perceive all options” type, he can just run through his proofs-by-cases quickly enough that it seems J. As a department head, he does have to use some J behavior with his staff by virtue of the position (the same phenomenon can be seen with the Gil Grissom INTP character from CSI).
If you want more: check the massive Fe reaction he pulls at Cuddy’s place in the season 7 finale. Also, listen carefully to his one-liners, a very INTP sense of humor!