I read a theory somewhere here that went along the lines of Sasuke being able to cast a "Mini Infinite Tsukyomi" kind of like the IT Obito cast in Road To Ninja (yes I know it's not cannon). His pattern is close to the 3rd eye that JuubiJin Madara had but it was missing 3 tomoes I believe. That eye was capable of casting IT so it's possible Sasuke's eye can cast a lesser IT. Remember it's just a theory.
Soo going on the assumption that this is true, it's possible that Hagoromo wanted to give Naruto & Sasuke alot of power in hopes that they would purify the Indra VS Ashura hate cycle. Which they did. Other then the theory though, I have no idea why Sasuke would have that rinnegan.