I don’t personally care whether or not Prince Harry goes to Iraq. Or whether he throws a royal tantrum and resigns if he is banned from going.
But this whole affair raises one question in my mind. If you join the army, then you are trained to be soldier. That becomes your job. If it’s possible that you’re going to be prevented from doing that job for some reason then perhaps you should declare that possibility when you sign up. And if it’s likely that you’re not going to be able to get involved in the day to day work of a soldier (like going off to parts foreign and potentially being put in mortal danger) then perhaps the army should think twice before spending (some might say “wasting”) money on training you to do things that you won’t ever be allowed to do.