The movie needs to solidify Kirk as being worthy of command, rather than being a punk kid who bluffed/lucked his way into the captain's chair. A good way to do this is for a villain who humbles the cocky kid, who then comes back to a victory that is clearly deserved the way nothing in the last movie really was.
And Spock also needs more on his character arc, the repercussions of the destruction of Vulcan, wherever that takes him (no place good, I'm guessing).
If the villain can be the catalyst for those character arcs, then good. I don't see the villain, whoever he is, as being important to the ongoing story (what are the odds he'll even survive the movie?) But that just means the villain is being used to further more important goals, not that it's all about him.
They've got more than enough important material set up by the last movie, they really don't need the villain do anything more than be a catalyst for Kirk, Spock and maybe if we could get some meaty character stuff for Uhura and McCoy, that would be great.
Given all the stuff this movie needs to tackle, I don't see how Khan could be shoehorned in. We can't assume his backstory is the same, or that the audience will know much about it, and going over all that stuff will take up too much time. Maybe this Khan is completely different and doesn't require a big backstory, but then he's not really Khan anyway. He's a new villain with an old name.
Given what the movie needs to do, the most "logical" villain is yet another Romulan. Kirk can be challenged by any villain who poses a competent threat, but Spock's arc would be most readily propelled forward by a Romulan.
