So indeed our American friends did and does much in Iranian interests.
Iran has been the accidental beneficiary of the US overthrowing two of its worst enemies: The Taliban in Afghanistan and Saddam Hussein in Iraq. Tehran did not have to do much to harvest the benefits to itself of US policy since 2001. A democratic election in Iraq, as happened in 2005, was bound to benefit Tehran by bringing Shia religious parties to power in Baghdad. The real problems of the US and Britain in Iraq are indigenous and only marginally connected to Iran.