Soviet Union containment policy. Same reason CIA didn't really care about the 1979 revolution (until it was too late): in their back channel talks with Khomeini, he told them that he wasn't opposed to US interests and wasn't going to let the Soviets in. That was exactly what the US wanted to hear.

The real head-scratcher is why the US refused to extradite the Shah back to Iran for trial. What a different world we'd be in right now: the hostage crisis never would've happened. Moderates would've been empowered. Iran's completely valid historical grievances would've been addressed. Who knows, maybe the Iran-Iraq war never would've happened. The US wouldn't have provided WMDs to Saddam Hussein. No Gulf War I and II.

The British blockade probably did more for the downfall of Mossadegh than the US influence on the Shah. Iran's economy was severely impacted by the blockade and this allowed the Shah to gain support within the Iranian government for a coup. The US decided to support a coup because it was feared that a collapse of the Iranian economy would open the door to communist revolutionaries, and the US was not prepared to go against Britain and try to stop the blockade. I have wondered, however, if the outcome of the Iran situation in 1953 affected Eisenhower's judgment about the Suez crisis in 1956.

By 1979 it was no longer possible to marshal public anger towards the UK whose empire had been completely dismantled. Meanwhile, the US continued to support the Shah's regime by selling weapons until 1979, and this was probably at least as important as the coup for the image of America as a public villain during the Islamic Revolution.