When Kakashi got the eye, it was 2T right? Maybe the eye can only be changed if it is advanced further. If that's true, Kakashi's 2T to MS would make sense while Nagato (whom only knew the power of the Rinnegan) could not revert it to a lesser form or even recognize that there was one.
However, this doesn't explain why Kakashi didn't revert back to 2T to conserve chakra in low stamina situations, or while he was just walking around Konoha with it covered or not. At the same time, maintaining 3T may have been Kakashi's choice. It could be possible that the difference in the chakra usage from 2T to 3T was negligible to him, or he just really preferred/got used to 3T.