Actually that would not be a good thing. Remember there was a time, up until the late 70s, when Iran used to be one of our biggest allies (the biggest in the M-E after Israel). Goodness, we even went as far as to sell/give them F-14 TomCats. Anyways, the Shah of Iran was nothing more than a despot, and we supported him and ensured he kept power (and all the while he was crushing his people).
It was so easy for the Ayatollahs to spur the rabble to action, paint the US as the 'evil puppeteer' behind the scenes, and after the revolution Iran went from friend to public enemy.
The thing about Iraq is this .....any government that takes over after June 30th must be better than what was there under Saddam. If it isn't it will be all too easy for the clerics to paint a picture that depicts the US as nothing more than people who came to disrupt their country (the old better the devil you know ...). That might be why GW is emphasising that the government should be democratic.
I personally feel the whole 'hearts and minds' thing is a difficult thing to do in the ME, but when it comes to Iraq we really have to ensure it is as much a success as possible. Coupe de tats, especially those that happen to be taken over by bad people who at the same time happen to be pro-American, would be a veritable poison-pill to anything we are trying to do in Iraq.