In the Bryan Burk interview covered on trekmovie.com (link, below), Burk says, "[Cumberbatch] kind of made Harrison his own. Particularly when we cast him -- the writers went back and specifically tailored it for Benedict."
So, maybe the character wasn't Harrison to begin with. Maybe it was Khan.
As has been pointed out many times, four actors said to be considered for the villain before Cumberbatch, Benicio del Toro, Edgar Ramirez, Jordi Rolla, and Demian Bichir were at least reminiscent of Montalban's Khan. Three were also the right age for a thawed Khan (mid-forties).
It's been said Cumberbatch was auditioned as more or less an inspiration, and he knocked their socks off. At the same time, they realized he probably couldn't be Khan with any sense of believability (that's been debated here, but I've always wondered why the net was originally cast so small ethnically, as if looks did matter for the part, then it turns out they end up with the least Khan-looking actor of the lot).
So as Burk says, they tailored the character to Cumberbatch, (speculation begins here ==>)
and made him, "John Harrison." They gave him his own backstory that gave him basically the same motives and goals as what had been written for Khan (can't change too much). It could be that Khan’s presence looms in this movie thematically even if the character doesn't appear.
Here's the link to the story about the interview: