There's a wrinkle.
Iraq is a sovereign nation. An Israeli airstrike can't happen without IRAQ authorizing overflight, or the US overriding the government whose sovereignty we're supposed to be protecting in order to favor the Jews flying over a Shi'ite country to hit the Shi'ite homeland.
There's a whole lot of bad in that.
Sure, the US could force Iraq to accept the overflight, but at that INSTANT, the mood of the allied Iraqis would shift to resentment, and the Shi'ites themselves would be seeking a much quicker American exit than they currently are. Once the government of Iraq asks the US to leave, we have to go, or our entire justification for being there falls utterly to ashes, we become a naked colonial power, and we face an insurgency that involves everybody.
We can't let the Israelis overfly Iraq without Iraqi permission, which they will not give. We can't override Iraq without losing them as an ally and rendering our entire war there for nought. At the end of the day, American forces and the American project's success in Iraq is more important than Israel. Because Iraq is US. Israel is a foreign country. We are more important than them, to us (or better be).
Didn't see a single thing in your post with which to disagree.