Did we really overthrow Iran's government? I'm not so sure. I've read in multiple places that Operation Ajax was a failure and Shah Mohammad Reza Pahlavi had to flee. So the CIA ordered that operation ajax cease, but rogue agent Kermit Roosevelt continued. And exactly how much did Roosevelt's actions impact things anyway with the clerics already stirring things up against Mossadegh?
Last but not least, keep in mind that when the CIA "admitted" to it in 2013, it was during Obama's reign. It's possible that this "admission" was part of Obama's 8 years of apologizing for America's existence.
So I'm not as sure as I used to be that we overthrew Iran's government.
Suggested reading:
Countercoup: The Struggle for the Control of Iran (1979) by Kermit Roosevelt Jr.
Regime Change in Iran: Overthrow of Premier Mossadeq of Iran, November 1952 – August 1953 by Donald N. Wilber.
CIA contract employee, Iran specialist, and one of the principal planners. He helped draft the operational plan in Cyprus with British counterparts and later wrote this detailed after-action report for the agency while events were still fresh. The declassified document has been published in book form and is a dry, operational chronology rather than a personal memoir.
Something Ventured by Christopher Montague “Monty” Woodhouse.
Woodhouse was the key British MI6 officer in Tehran who helped initiate and shape the British side of the plot (Operation Boot)