1. The plot to overthrow Mosaddegh went off exactly as planned. Ignoring any moral factors, it was very a impressive operation. I wouldn't doubt that CIA took as much responsibility for it as they could.
2. It is true that Mosaddegh had broad popular support, but he was also opposed by a large fraction of the population (eg. the mass protests that called for his head).
I'll take back the comment that he wouldn't have been able to maintain rule (I'll readily admit I can't predict the future). However, my point is that the CIA didn't create a coup out of thin air.
What the CIA did in Iran was provide operational support for the anti-Mosaddegh forces. Not really all that different than what the CIA did in Afghanistan during the war with Russia.