I don't like flying over the western parts of Iraq these days and I believe, I'm not the only one. I said no to doing it and we got a different routing.
Overflying Iran, however, is absolutely safe and their ATC standards are high.
The fact is, nobody (or maybe somebody...?) knows for sure what sort of threats exist on the ground overhead Mossul etc..
Nobody wants to be reminded of the Donbass, it appears.