I say Cumberbatch is Starfleet's attempt at a 23rd century Augment (hence the Khan rumors and him being in a Starfleet uniform in the leaked footage). It will go horribly wrong.
Sounds like a complicated setup. Remember, the audience will mainly be comprised of people for whom "augment" and "eugenics" are meaningless, eye-glazing technobable, and who have plunked down their twelve bucks to see exciting zap-bang action, not listen to characters yak yak yak for the purpose of setting up a plotline.
Gary Mitchell is wonderfully action-movie-ready: Starfleet officer gains power of a god, goes crazy, zany hijinks ensue! That can be explained quickly enough that nobody will get bored and go to the lobby for popcorn.
After all, the important part is "it will go horribly wrong." Why take more time than necessary getting to that point? The way you described Khan is just an unnecessarily complicated version of Mitchell anyway.