You are correct.
And taking out Sadam Hussein was a terrible mistake for the same reasons you state about the Shah of Iran.
Yep. BIG mistake. Government of the ME needs to be left in the hands of “bastards.” Trying to introduce democracy there was a bad idea - with the exception of Israel there is no one in the ME capable of democratic self-government and I doubt there ever will be.
The big mistake with Iraq was not creating three separate states; Sunni, Sharia, and Kurds, with some consortium to run the oil fields and refineries for the benefit of the three states.