But the chances of a smooth transition are higher if the people of the country mange that by themself, instead of foreign forced change, where many suspect the motives are different.
You are ignoring that the US is not the only forign power. In a time of state collapse, other state will always have the upper hand.
Even if the US had not tried to create their kind of government, Iran sure as shit was trying to get their guys in.
So for the US its not about a question about US control, Iraqi control. Its a question of US control or Iranian control.
In this case they supported mostly the same groups, ironically. Iran did en up with the upper hand by far in Iraq, meaning the US achived LITERALLY the opposite of what they wanted to achive.