In terms of the actual presence of a government, what's the difference between not choosing a government and allowing it to continue? 
You are wrong! The Iranians didn't choose this type of Government and the former president carter didn't back the Shah and the country fell in hands of the hardliner mullahs.
Try to read more about Iran!
The Iranians didn't choose this type of Government and the former president carter didn't back the Shah and the country fell in hands of the hardliner mullahs.You are right.
In terms of the actual presence of a government, what's the difference between not choosing a government and allowing it to continue?
How am I wrong? They wanted an Islamic revolution and they got it. They are welcome to it. If the Iranians had liked the Shah well enough they would have kept him.