Kishi wouldn't kill him before someone else knows how Minato's team was played by Madara because that will show why Obito deserves redemption. I think Obito is playing dead until BZ lets his guard down enough for Obito to let Kakashi know that Madara played them all and to use the last of his life to help the alliance.
Just like Naruto and Sasuke are going to redeem Itachi in everyone's eyes when the war is over with their stories of him, Obito will have the same redemption before he dies.