Board Thread:Naruto Discussions/@comment-30881771-20170815144139/@comment-734582-20170817143844

Ravenlot 27 wrote: Not really, we have a clear evidence that Shin's cloning was happening quite a while before this, since Oro stated that he transplanted Shin's arm to Danzo along with the Sharingans and Hashi's cells within it, meaning it transpired during the times when Oro was still a Konoha shinobi. There is no reference to when the cloning started. We know that arm contains Sharingan and Hashi cells, so cloning wasn't the only experiment on Shin. It's entirely possible that the cloning only happened after Orochimaru's rebirth. Or it could've happened after Orochimaru captured Sasuke, as Orochimaru was hellbent on making Sasuke his vessel and so would not have taken a shin.

Either case would explain in a very reasonable way why he didn't take a Shin.