I suppose I ought to be pleased that a church in Baghdad has re-opened. But the goodness of that news is overwhelmed by the badness of the news in general about Iraq over the last few years. I am under no illusions about the wickedness of Saddam Hussein. However, the wickedness of a leader doesn't provide justification under law for intervention in the internal affairs of a nation, and the moral case for intervention is undermined by the indifference of the same leaders who intervened to wicked governments elsewhere in the world, and their own use of morally unacceptable means in pursuit of their aims.
In addition to which, the situation in Iraq is now far less sympathetic to Christianity than it was under an authoritarian regime - and if in the fullness of time the democracy decides to establish an Islamic regime, or if the country decides that balkanisation is the way forwards, or if the new regime is unable to prevent a slide into anarchy - all of which options seem as likely as the "dream scenario" of a stable, tolerant, liberal democratic government - then the environment for Christianity will have been substantially weakened.
The intervention of the US/UK and other members of the international community in Iraq was not a "Christian" action - the Christian message is not directed towards international politics, and does not give guidance in this area to leaders of nations who happen to be Christians, other than the general principles (things like acting justly, loving mercy, walking humbly before God).