Regarding Mossadegh...
I think people keep on missing the whole background basis of colonialism that is the basis for the oil nationalization, and the hatred towards the West...
This doesn't just apply to Iran, it also applies to other colonized and quasi-colonized states.
Do you know why the Chinese see the Japanese as worse than the CCP, despite the CCP's atrocities? It's because at least the CCP had legitimacy as rulers of China, because their basis was indigenous origin. They may have gotten support from the USSR, but their rule was perceived as rooted as a
Chinese thing, rather than a foreign one. And considering what came afterwards with the Sino-Soviet split, they weren't puppets of other powers.
The Japanese, on the other hand, were seen as foreign rulers who wished to subjugate the Chinese under their rule, and who did so through horrific atrocities that rivaled the Nazis, which was unacceptable to the Chinese. This was different from the previous conquest dynasties (like the Qing), due to the rise of Chinese nationalism (along with the fact that these dynasties took pains to style themselves in the Chinese manner, though that is of lesser importance).
This is why I think is the reason that despite Mossadegh's errors and foibles, the coup was still a bad idea, as it robbed the Shah of any legitimacy from the view of the Iranians. It's like why putting Puyi as the leader of Manchukuo didn't work-people don't see the Shah's rule as an
Iranian one, but as a foreign-imposed one, like Puyi in Manchukuo was seen as a Japanese puppet (which he was).
Mossadegh, on the other hand, was seen as an Iranian leader who was deposed by the foreign powers in exchange for their preferred sockpuppet. And in the view of the Iranians, the coup robbed them of their agency to do what they wished-to choose their own leaders who did policies that they supported, which in this case was oil nationalization, which was a highly emotional one for Iranians as they saw the deal they had with the British as utterly unfair, where they got gypped out of the $$$ (leading to the rise of Iranian nationalism).
Of course, there were complications and the like, but the fact of the matter is, the Shah wasn't seen as legitimate because of the coup...
The coup also added to this sense of injustice that the Iranians, like all colonized/quasi-colonized peoples, have towards the West, in that "Why is it that if the West does x, it's fine by them, but when we want to do the same thing, it's not allowed?"
This is seen to this present day with the Iranian nukes, where they see the West as trying to screw them up like with the oil, saying "Your worries about our use of nuclear energy is the same as what your worries over our ability to handle our oil resources back then, and back then it turned out to be bullshit!"
It is no coincidence that one of the things that the Islamist regime did was to nationalize the oil resources, like they did back then.
(This also explains why these countries are more supportive of Russia and China, in that they see them as less hypocritical by comparison to the West).
There is this fundamental sense of injustice that underlines all of this...as explained by
Pankaj Mishra, author of the book
From the Ruins of Empire.