Modernization can happen, but only if it's not visibly pro US.
On the contrary:
In August 2013, sixty years afterward, the U.S. government formally acknowledged the U.S. role in the coup by releasing a bulk of previously classified government documents that show it was in charge of both the planning and the execution of the coup, including the bribing of Iranian politicians, security and army high-ranking officials, as well as pro-coup propaganda. The CIA is quoted acknowledging the coup was carried out "under CIA direction" and "as an act of U.S. foreign policy, conceived and approved at the highest levels of government".
Very similar to what happened with Vietnam and the Diem regimen.
No, it (and the British who actually started trying to pull off a coup first) paid people and deployed propaganda from multiple different angles, and including false flag operations, to energize multiple, mutually antagonistic factions in order to destabilize the Mossadegh regime; a lot of the anti-Mossadegh opposition was organized crime groups paid by the CIA to put up a front as political opposition. They didn't care about the politics; they did care about the money.
Heck, even the Shah—the monarch who superficially seized total power in the coup—was opposed until the CIA threatened to depose him as well if he didn't go along.