This is likely true, however there are a lot of strings if you pull on anything associated with the Cold War. Even without leaning on domino theory and assuming that Iran was better with a democratically elected government, I don't think it's conclusive to say that "If the US hadn't been involved in Iran, the world as a whole would have been a better place." I think Poland, Hungary, and a lot of Eastern Europe are probably happier without the Soviet Union?

As a friend in Jordan said, sometimes democracy isn't the best first step. And I'd argue that both Atatürk and Nasser played pretty close to the line as well.