wouldn't Kahn get put in the tribble...?

Kahn. What made him memorable in the second movie was his personal history with Kirk and that doesn't exist here. In Space Seed he was just another villain of the week but Kirk having stranded him on a planet that became inhospitable leading to the death of his wife and followers gives him a reason to want revenge.

Here we're presented with a character who, off screen was defrosted from suspended animation after 300 years and used by Admiral Marcus whilst his people are held hostage in stasis tubes. No reference is given to the eugenics wars and very little is said about his background other than that he is a genetic superman.
He shares very little with Ricardo Montalban character which begs the question why bother using him at all.  You can't just put a character like Kahn in a new story without loosing who he was. If your familiar with the original films the character doesn't make sense and if your a new comer it's just a random character we are told is the worst enemy the Enterprise will ever face.

There were a series of comics where old episodes were retold with the new Enterprise which was fun for a few issues but soon lost its novelty and I certainly don't enjoy the films doing it with scenes from other movies, line for line with characters swapped around and whilst some may argue that Wrath of Kahn is cheapened by The Search For Spock it's nothing compared to solving everything in the last 10 minutes with a magic tribble.

The film has some issues in the second hour that go beyond this but for me the film would be significantly improved if instead of Kahn Cumberbatch's character was called oh I don't know... Steve.