Sasuke is more useful not residing in Konoha, as he can then be more trusted by the underground criminal associates, as they will think he still has no ties with Konoha, and remember, Kakashi espoused the idea of Sasuke building a relationship with the evil forces in the shadow. Sasuke's usefulness is proven true when he seems to know every ounce of thing including the existence of a cabal such as Kara, even before Shikamaru fathomed such an organization existing. So Sasuke is more useful outside of Konoha. As he then becomes the sacred eyes Konoha, outside its confines. Konoha insiders will always know less obviously. Isn't that why Sai and Orochimaru are not the enemies of Konoha, despite their perfidious actions in the past? Even Danzou, with a history tainted by malicious actions was pardoned by Hiruzen, and Danzou himself considered himself the shadow hokage, which you should look up by the way, as that's actually a bona fide term.
Now Sasuke, being the ''shadow'' hokage, shouldn't be inside the confines of Konoha. Because he isn't the Hokage of the village. He's the shadow hokage, and as such, should be outside, playing the role of the protector. His job is not to reassure the safety of the village, but to make certain of its safety. There's a difference between Sasuke and Naruto's occupations, and Sasuke's gravitates towards enforcing safety.
