It is the US government's desire for the Iraqi people to...

It is the US government's desire for the Iraqi people to lead themselves, not for any outside power to be the leadership for Iraq in the future. There may be some transition period where the international community would have to help the Iraqi people put in place a representative government. But that is the goal, not for the United States, or any other nation, for that matter, who might be in such a coalition, if one is formed, to serve as the leader of the Iraqi nation.