Possible explanation (to the whole asspull/episode):
Obito not using Susano'o but Kakashi suddenly does
Anyone remember how Obito was supposed to die from the Bijuu extraction? It's possible that Obito had rikudou powers left in him from being the Jin but could not use them or Susano'o because he was on the verge of death.
Obito traveling to the Real World after death
It's possible that Obito knew all along how to reach the pure world dimension with his sharingan, but would die if he ever went there with it, so he never went when he was alive. But after death he knew how to get back to the impure world dimension (i.e. reality) temporarily.
Obito transplanting eyes which were clearly disintegrated to dust...
The pure world is also "physical" in some sense and everyone gets a new sort of body when they die. So dead Obito did have a legitimate pair of sharingans. As for how he transferred them, we've already known chakra can be passed down by the dead, as well as seals, jutsu, etc. This just revealed something new. But I'm guessing this means dead Obito won't ever have the sharingan again, since the real world ones burned to dust, and Kakashi has the pure-world ones.
Kakashi suddenly wielding Perfect Susano'o from the get-go
...Yeeeeaahh... I got nothing for that.
Except maybe inheriting the development of Obito's sharingan. So maybe Obito was already at a level of mastery and hatred where he could have pulled out Perfect Susano'o but he was just missing the other eye. If you think about it, his hatred was pretty hardcore so doesn't it seem odd that he never used Susano'o? He definitely would have had a stabilized one if he could. And we know that the powers of the sharingan are transferred to the new user, (like Sasuke getting Amaterasu) without needing whatever effort it took them to get to that point.
Mystery Solved!!!