There is a not insignificant (at least by noise level) portion of the Iranian Diaspora that want the US to invade specifically to install Reza Pahlavi as King. I know because they are harassing my wife on social media when she posts her position which is as you described. You are right in that the majority don't want a war like this, but Royalists specifically (including the prince of nothing himself ) seem to actually believe that this would be a good thing.

You only have to look at what happened around Huda Beauty, when their Iraqi owner said the same thing you are saying.