He already had immense power prior to the coup. At best, his autocratic power was strengthened. Calling him installed by the US is a misrepresentation.
Iran was not a British-style constitutional monarchy. The Shah was not a ceremonial position. His father ruled with even more power than he did. He was just an absentee ruler for the first part of his rule until someone tried to assassinate him.
Never mind that Prime Minister Mosaddegh had dissolved parliament and had been ruling by decree for a year also acted as an autocrat. Even his own party turned against him for abuse of power.
At best, one could argue the British installed the Shah. They are, after all, the people who made him Shah in the first place.
I'm unsure as to how the US installed him in 1953. He had been Shah for 11 years.