The big picture is not irrespective of the motive. The thingie Mycroft brought up. Maybe he did not use the word motive. That is what he discussed anyway. What makes the P tick.. tick tick.. what makes the J tick..
And he said the P is not utilitary- in his own words. In for the game.
Hence it is a question of motive.
And the motive is about freedom.
This is why the Ps are often artists.
For Scherlock, the detective thing was an art. He was an artist.
What a good artist he was.
What does the artist do?
He sees the picture. The P thing.
But there are artists who see behind the picture. They are NPs.