I checked the map after reading the article and before posting my comment just to keep my geography straight. Even if Saudi Arabia is a consideration, they are going through Jordan, although it looks there might be an intersection point at the southern most border of Israel.
I think it’s more reliable and likely the U.S. would allow or possibly escort through Iraqi airspace. I didn’t mention it originally because I figured it would be a given.
It’s all conjecture until the planes are in the air though.
If they went through Iraq, they would have to tell the US what they are doing. You are assuming that the Prez will give clearance. I know the US military would be happy to escort them all the way to Tehran but the bureaucracy might have other ideas.