Overflight is a non-issue. Their controllers speak better English than most of world, very professional. Never had an issue. On my last trip the Capt was dual Iranian/Us citizen, also a good guy to fly with. Obviously he got out circa 1979. Interesting to hear his take on things today. He was not worried about setting down there in an emergency, but he spoke Farsi. They would probably give him more scrutiny than I would get. Given a choice, I would not divert there unless I absolutely had to. You never know when somebody wants to make a statement and use you as leverage.