The Qajars are a really complex dynasty. They are a Persianized Dynasty of Oghuz Turkic origin. Except for the Shah and his heir, nobody else of the Dynasty is seen outside in Public Life. Today they are rather disliked in Iran (53% dislikes the monarchy, 29% likes the monarchy, 18% is unsure...). But the Shiites and Shia Clergy like them for their religiosity and efforts for the Shias over the world. Their attempts to become popular by renaming the state to Iran to include all ethnicities are still not really looked on positively. There was a small rise in popularity when the Shah send volunteers to the Arab States in their war in Palestine. But over all they are still not really liked.
There was a chance to be deposed in 1921 but Reza Khan, the leader of the coup forces, was arrested at State intelligence reporting him. What if his coup succeeded? Would an Iranian Republic fair better? Or would it be one of another Military Dictatorship like Syria, Iraq or Pakistan?