Maybe in order to use 6PoP you have to have both Rinnegan eyes. Since obito has only one, I get the impression that he implanted it only in order to control the previous jinchuuriki. Also, it was stated by Kakashi that jinchuuriki's bodies dont use Pein's skill because it consumes much chakra and Obito did not oppose, here is the page
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From the beginning Obito couldn't have resurrected Rin even if he had rinnegan, because if he could, that would mean that he would be ablo to resurrect Madara (he died after Rin so time doesn't matter) so Madara wouldnt have to give his eyes to someone unknown as Nagato.