> When it imposes a new government on countries (like Iraq) it chooses a parliamentary system.

I'd avoid reading too much into this. The US simply tries to avoid making too many major changes to the system of government and Iraq was familiar with a parliamentary system already.

The Empire of Japan was a parliamentary semi-constitutional monarchy. Today it is a parliamentary constitutional monarchy. That doesn't mean the US loves kings/emperors.

By contrast, the Dominican Republic stayed as a presidential system.