This is sort of a bad and inaccurate summary of a much more complicated situation. Mossadegh was trying to dissolve parliament and was in conflict with the Shah before the British got involved. The Shah was already planning to try by constitutional means (which he had legal power to do) to remove Mossadegh. Would he have done it without British and US backing, is a debate for historians.
I don’t think any serious post WWII historians would agree with you. There was a concentrated effort by the UK and US to displace Mossadegh, who was democratically elected by the way. At the very least it disproves your unspoken assertion that the Iranians are primarily to blame for their problems when it’s been proven that the most powerful intelligence agencies on the planet were actively destabilizing their society so that oil revenue would continue flowing into western pockets.