> not because the facts of the US backed coup damaging Iran are at all in dispute.
I mean, they are, GP just admitted they stand corrected[0] and "democratically elected government" of Mossadegh is factually incorrect. Other comments have pointed out he was installed not by the people, but by the Shah and Majles, stopped 1952 elections when they didn't go his way, then tried to dissolve parliament and vest power solely in himself
In the events that followed his popularity rose and he tried to gather a government but was blocked by the shah, which made him even more popular, to the extent that the armed forces backed off from containing the demonstrations. It's against this background he sent a bill to the majlis that would give him six months of emergency powers to push through with his political program and the nationalisation, which was approved.
After those six months he asked for another twelve months and got it, but his base had started to wither away and allies switched sides because the reforms didn't have enough effect fast enough in the international climate they were in. I.e. trade boycott and foreign influence operations and so on, which of course hurt his constituents. Some of his allies were also afraid that he might turn against them, hence they turned on him.
Churchill convinced Eisenhower that Mossadegh were going to deport the shah, and then they launched the coup.